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0FC0000000232B7F9D27>I E end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300dpi
TeXDict begin

%%EndSetup
%%Page: 57 1
57 56 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)0 42 y Fy(26.)52 b(Examples)0
158 y FF(The)14 b FG(Dash)p FF(,)e FG(Dashto)f FF(and)j
FG(Mono)e FF(cell)h(t)o(yp)q(es)h(in)f(some)f(of)h(these)h(examples)e
(use)i(the)g FG(arrsy10)e FF(fon)o(t:)17 b(See)d Fw(x)q
FF(14)e(and)h FG(\\arrsy)0 208 y FF(in)g Fw(x)q FF(25.)k(Also,)d
FG(\\bb)f FF(in)o(v)o(ok)o(es)g(the)i(bbm)d(family)f(of)i(fon)o(ts.)-79
299 y Fr(1)62 b Fx($$)-79 349 y Fr(2)g Fx(\\grid=.75c)o(m)-79
399 y Fr(3)g Fx(\\Diagram)-79 448 y Fr(4)g Fx(A')176
b(&)137 b(&)19 b(\\rTo)f(^{f'})g(&)137 b(&)19 b(B')529
b(\\\\)-79 498 y Fr(5)278 b Fx(&)19 b(\\rdTo)f(<a)h(\\dh{2pt})o(&)e(&)
137 b(&)176 b(&)19 b(\\rdTo)f(_b)215 b(\\\\)-79 548 y
Fr(6)62 b Fx(\\dTo)18 b(<{g'})g(&)137 b(&)19 b(A)196
b(&)137 b(&)19 b(\\dTo)f(<{h'})g(:{.25})-79 598 y Fr(7)886
b Fx(\\rTo)18 b(^f)h(:{.25})e(\\br)-79 648 y Fr(8)1043
b Fx(&)195 b(&)20 b(B)137 b(\\\\)-79 697 y Fr(9)1455
b Fx(\\\\)-95 747 y Fr(10)61 b Fx(C')176 b(&)137 b(&)19
b(\\rTo)f(^{k'})g(:{.75})f(\\dTo)h(<g)h(:{.25})e(\\br)-95
797 y Fr(11)689 b Fx(&)137 b(&)19 b(D')117 b(&)195 b(&)20
b(\\dTo)e(>h)h(\\\\)-95 847 y Fr(12)277 b Fx(&)19 b(\\rdTo)f(_c)h
(\\dh{.5pt)o(}&&)134 b(&)176 b(&)19 b(\\rdTo)f(_d)215
b(\\\\)-95 897 y Fr(13)277 b Fx(&)137 b(&)19 b(C)196
b(&)137 b(&)19 b(\\rTo)f(^k)h(&)195 b(&)20 b(D)137 b(\\\\)-95
946 y Fr(14)61 b Fx(\\endDiagra)o(m)-95 996 y Fr(15)g
Fx($$)889 1135 y
gsave
 889 1135 a 889 1135 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 889 1135 a 741
1146 a Fw(\000)-21 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)-21 b Fv(\021)889 1135 y
grestore

889 1135 a 889 1135 a
gsave
 889 1135 a 889 1135 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 889 1135
a 888 1123 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 888 1123 a 873 1117 a Fu(f)892 1105 y Ft(0)888
1135 y
grestore
 888 1135 a 800 1224 a
gsave
 800 1224 a 800 1224 a
currentpoint currentpoint translate -2797018 neg 2797018 atan rotate
neg exch neg exch translate
 800
1224 a 698 1234 a Fw(\000)h(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)
h(\000)-19 b Fv(\021)800 1224 y
grestore
 800 1224 a 800 1224 a
gsave

800 1224 a 800 1224 a
currentpoint currentpoint translate -2797018 neg 2797018 atan rotate
neg exch neg exch translate
 800 1224 a 800 1236 a
currentpoint currentpoint translate 2797018 neg 2797018 atan rotate
neg exch neg exch translate
 800 1236
a 782 1249 a Fu(a)800 1224 y
grestore
 800 1224 a 1154 1224 a
gsave
 1154
1224 a 1154 1224 a
currentpoint currentpoint translate -2797018 neg 2797018 atan rotate
neg exch neg exch translate
 1154 1224 a 1052 1234 a Fw(\000)-13
b(\000)k(\000)g(\000)g(\000)g(\000)g(\000)d Fv(\021)1154
1224 y
grestore
 1154 1224 a 1154 1224 a
gsave
 1154 1224 a 1154 1224
a
currentpoint currentpoint translate -2797018 neg 2797018 atan rotate
neg exch neg exch translate
 1154 1224 a 1149 1236 a
currentpoint currentpoint translate 2797018 neg 2797018 atan rotate
neg exch neg exch translate
 1149 1236 a 1134 1257 a Fu(b)1149
1224 y
grestore
 1149 1224 a 711 1313 a
gsave
 711 1313 a 711 1313 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 711
1313 a 553 1323 a Fw(\000)c(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)g(\000)-15 b Fv(\021)711
1313 y
grestore
 711 1313 a 711 1313 a
gsave
 711 1313 a 711 1313 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 711
1313 a 705 1325 a
currentpoint currentpoint translate 5594036 neg 0 atan rotate neg exch
neg exch translate
 705 1325 a 677 1335 a Fu(g)694 1323
y Ft(0)705 1313 y
grestore
 705 1313 a 1066 1313 a
gsave
 1066 1313 a
1066 1313 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 1066 1313 a 907 1323 a Fw(\000)f(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)
-16 b Fv(\021)1066 1313 y
grestore
 1066 1313 a 1066 1313 a
gsave
 1066
1313 a 1066 1313 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 1066 1313 a 983 1325 a
currentpoint currentpoint translate 5594036 neg 0 atan rotate neg exch
neg exch translate
 983 1325 a
952 1335 a Fu(h)971 1323 y Ft(0)983 1313 y
grestore
 983 1313 a
1066 1313 a
gsave
 1066 1313 a 1066 1313 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 1066 1313 a 889 1313
a
1 setgray
 889 1313 a 912 1323 306 21 v 1066 1313 a
grestore
 1066 1313
a 1066 1313 a
gsave
 1066 1313 a 1066 1313 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 1066 1313 a 912
1323 a Fw(\000)h(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)-15 b Fv(\021)1066 1313 y
grestore

1066 1313 a 1066 1313 a
gsave
 1066 1313 a 1066 1313 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 1066
1313 a 989 1300 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 989 1300 a 979 1294 a Fu(f)989 1313
y
grestore
 989 1313 a 889 1490 a
gsave
 889 1490 a 889 1490 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 889 1490
a 742 1500 a Fw(\000)-23 b(\000)-9 b(\000)h(\000)f(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)-22 b Fv(\021)889 1490
y
grestore
 889 1490 a 889 1490 a
gsave
 889 1490 a 889 1490 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 889 1490
a 961 1477 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 961 1477 a -15 w Fu(k)965 1465 y Ft(0)961
1490 y
grestore
 961 1490 a 889 1490 a
gsave
 889 1490 a 889 1490 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 889
1490 a 711 1490 a
1 setgray
 711 1490 a 730 1500 310 21 v 889 1490
a
grestore
 889 1490 a 889 1490 a
gsave
 889 1490 a 889 1490 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 889 1490
a 730 1500 a Fw(\000)-14 b(\000)-9 b(\000)g(\000)h(\000)f(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)c Fv(\021)889 1490
y
grestore
 889 1490 a 889 1490 a
gsave
 889 1490 a 889 1490 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 889 1490
a 807 1502 a
currentpoint currentpoint translate 5594036 neg 0 atan rotate neg exch
neg exch translate
 807 1502 a 790 1513 a Fu(g)807 1490 y
grestore
 807
1490 a 1243 1490 a
gsave
 1243 1490 a 1243 1490 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 1243 1490
a 1084 1500 a Fw(\000)g(\000)k(\000)g(\000)g(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)c Fv(\021)1243 1490 y
grestore
 1243
1490 a 1243 1490 a
gsave
 1243 1490 a 1243 1490 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 1243 1490
a 1239 1477 a
currentpoint currentpoint translate 5594036 neg 0 atan rotate neg exch
neg exch translate
 1239 1477 a 11 x Fu(h)1239 1490 y
grestore
 1239
1490 a 800 1578 a
gsave
 800 1578 a 800 1578 a
currentpoint currentpoint translate -2797018 neg 2797018 atan rotate
neg exch neg exch translate
 800 1578 a 698
1589 a Fw(\000)-23 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)
-22 b Fv(\021)800 1578 y
grestore
 800 1578 a 800 1578 a
gsave
 800 1578
a 800 1578 a
currentpoint currentpoint translate -2797018 neg 2797018 atan rotate
neg exch neg exch translate
 800 1578 a 797 1591 a
currentpoint currentpoint translate 2797018 neg 2797018 atan rotate
neg exch neg exch translate
 797 1591 a 782 1603
a Fu(c)797 1578 y
grestore
 797 1578 a 1154 1578 a
gsave
 1154 1578 a
1154 1578 a
currentpoint currentpoint translate -2797018 neg 2797018 atan rotate
neg exch neg exch translate
 1154 1578 a 1052 1589 a Fw(\000)-14 b(\000)-9
b(\000)g(\000)h(\000)f(\000)g(\000)c Fv(\021)1154 1578
y
grestore
 1154 1578 a 1154 1578 a
gsave
 1154 1578 a 1154 1578 a
currentpoint currentpoint translate -2797018 neg 2797018 atan rotate
neg exch neg exch translate
 1154
1578 a 1149 1591 a
currentpoint currentpoint translate 2797018 neg 2797018 atan rotate
neg exch neg exch translate
 1149 1591 a 1132 1611 a Fu(d)1149
1578 y
grestore
 1149 1578 a 1066 1667 a
gsave
 1066 1667 a 1066 1667
a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 1066 1667 a 913 1677 a Fw(\000)d(\000)-9 b(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-16 b Fv(\021)1066
1667 y
grestore
 1066 1667 a 1066 1667 a
gsave
 1066 1667 a 1066 1667
a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 1066 1667 a 1065 1654 a
currentpoint currentpoint translate 0 neg 5594036 atan rotate neg exch
neg exch translate
 1065 1654 a -9 w Fu(k)1065
1667 y
grestore
 1065 1667 a 690 1146 a FB(A)721 1129 y Fs(0)1043
1146 y FB(B)1076 1129 y Fs(0)873 1323 y FB(A)322 b(B)689
1500 y(C)722 1483 y Fs(0)1042 1500 y FB(D)1077 1483 y
Fs(0)872 1677 y FB(C)h(D)0 1852 y FH(G.)16 b(Bredon)p
FF(,)11 b FC(Intr)n(o)n(duction)16 b(to)e(Comp)n(act)h(T)m(r)n
(ansformation)f(Gr)n(oups)p FF(,)g(page)g(75.)-79 1944
y Fr(1)62 b Fx($$)-79 1993 y Fr(2)g Fx(\\Dg)-79 2043
y Fr(3)g Fx(F\\times)17 b(K\\times)g(U)98 b(&)19 b(\\rTo)f(^{\\rm)f
(proj})97 b(&)215 b(&)19 b(K\\times)e(U)157 b(\\\\)-79
2093 y Fr(4)62 b Fx(\\dTo)352 b(&)431 b(&)215 b(&)19
b(\\dTo)f(>{\\rm)g(proj})g(\\\\)-79 2143 y Fr(5)62 b
Fx(F\\times_K)16 b(\(K\\times)h(U\))i(&)g({})g(\\approx)d(F\\times)h(U)
j(&)f(\\rTo)f(^{\\rm)g(proj}&)f(U)196 b(\\\\)-79 2193
y Fr(6)62 b Fx(\\endDg)-79 2242 y Fr(7)g Fx($$)1012 2377
y
gsave
 1012 2377 a 1012 2377 a
currentpoint currentpoint translate 0 neg 7515619 atan rotate neg exch
neg exch translate
 1012 2377 a 885 2387 a Fw(\000)-21
b(\000)-9 b(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g
(\000)g(\000)-20 b Fv(\021)1012 2377 y
grestore
 1012 2377 a 1012
2377 a
gsave
 1012 2377 a 1012 2377 a
currentpoint currentpoint translate 0 neg 7515619 atan rotate neg exch
neg exch translate
 1012 2377 a 1033 2364
a
currentpoint currentpoint translate 0 neg 7515619 atan rotate neg exch
neg exch translate
 1033 2364 a 1003 2358 a Fr(pro)r(j)1033 2377 y
grestore
 1033
2377 a 774 2471 a
gsave
 774 2471 a 774 2471 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 774 2471 a 701
2482 a Fw(\000)i(\000)-9 b(\000)g(\000)g(\000)-18 b Fv(\021)774
2471 y
grestore
 774 2471 a 1250 2471 a
gsave
 1250 2471 a 1250 2471 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate

1250 2471 a 1178 2482 a Fw(\000)g(\000)-9 b(\000)g(\000)g(\000)-16
b Fv(\021)1250 2471 y
grestore
 1250 2471 a 1250 2471 a
gsave
 1250 2471
a 1250 2471 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1250 2471 a 1248 2459 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 1248 2459 a 10
x Fr(pro)r(j)1248 2471 y
grestore
 1248 2471 a 1122 2566 a
gsave
 1122
2566 a 1122 2566 a
currentpoint currentpoint translate 0 neg 4036624 atan rotate neg exch
neg exch translate
 1122 2566 a 1088 2576 a Fw(\000)d(\000)-9
b(\000)g(\000)g(\000)-18 b Fv(\021)1122 2566 y
grestore
 1122 2566
a 1122 2566 a
gsave
 1122 2566 a 1122 2566 a
currentpoint currentpoint translate 0 neg 4036624 atan rotate neg exch
neg exch translate
 1122 2566 a 1157
2553 a
currentpoint currentpoint translate 0 neg 4036624 atan rotate neg exch
neg exch translate
 1157 2553 a 1127 2547 a Fr(pro)r(j)1157 2566 y
grestore

1157 2566 a 671 2387 a FB(F)15 b Fw(\002)10 b FB(K)i
Fw(\002)d FB(U)318 b(K)12 b Fw(\002)e FB(U)639 2576 y(F)15
b Fw(\002)713 2582 y Fu(K)754 2576 y FF(\()p FB(K)e Fw(\002)c
FB(U)c FF(\))12 b Fw(\031)g FB(F)j Fw(\002)9 b FB(U)158
b(U)954 2770 y FF(57)p eop
%%Page: 58 2
58 57 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)-79 42 y Fr(1)62 b Fx($$)-79
91 y Fr(2)g Fx(\\joined)17 b(\\let\\labe)o(lst)o(yle)o(\\t)o(ext)o(st)o
(yle)-79 141 y Fr(3)62 b Fx(\\Graph{3cm)o(,2)o(}{3)o(cm)o(,4})-79
191 y Fr(4)g Fx(\\Line)18 b(\(0,0\))f(\(0,4\))h(<{f\(z,s\)})-79
241 y Fr(5)62 b Fx(\\Line)18 b(\(0,4\))f(\(2,4\))h(^{H\(z,t\)})-79
291 y Fr(6)62 b Fx(\\Line)18 b(\(0,0\))f(\(2,0\))h(_{*})-79
340 y Fr(7)62 b Fx(\\Line)18 b(\(2,0\))f(\(2,4\))-79
390 y Fr(8)62 b Fx(\\Line)18 b(\(0,4\))f(\(2,2\))h(_{\\;\\;H\(z,)o(0\))
e(=)j(f\(z,1\)})e(\\ro)-79 440 y Fr(9)62 b Fx(\\endGraph)-95
490 y Fr(10)f Fx(\\qquad\\qqu)o(ad)-95 540 y Fr(11)g
Fx(H'\(z,t,s\))16 b(=)-95 589 y Fr(12)61 b Fx(\\cases{f\(z)o(,2)o(s/\()
o(2-)o(t\)\))o(&)17 b(if)h($0\\le)g(2s\\le)g(2)h(-)g(t$\\cr)-95
639 y Fr(13)198 b Fx(\\cr)-95 689 y Fr(14)g Fx(H\(z,2s)18
b(-)h(2)g(+)g(t\)&)g(if)g($2)f(-)i(t\\le)e(2s\\le)f(2$\\cr})-95
739 y Fr(15)61 b Fx($$)263 1012 y
gsave
 263 1012 a 263 1012
a
currentpoint currentpoint translate 5594036 neg 0 atan rotate neg exch
neg exch translate
 263 1012 a 82 1022 a Fw(\000)-17 b(\000)-9 b(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)
-17 b(\000)263 1012 y
grestore
 263 1012 a 263 1012 a
gsave
 263 1012
a 263 1012 a
currentpoint currentpoint translate 5594036 neg 0 atan rotate neg exch
neg exch translate
 263 1012 a 263 999 a
currentpoint currentpoint translate -5594036 neg 0 atan rotate neg
exch neg exch translate
 263 999 a 147 1009
a FB(f)t FF(\()p FB(z)r(;)7 b(s)p FF(\))263 1012 y
grestore
 263
1012 a 440 834 a
gsave
 440 834 a 440 834 a
currentpoint currentpoint translate 0 neg 5594038 atan rotate neg exch
neg exch translate
 440 834 a 259 845
a Fw(\000)-17 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)-17 b(\000)440
834 y
grestore
 440 834 a 440 834 a
gsave
 440 834 a 440 834 a
currentpoint currentpoint translate 0 neg 5594038 atan rotate neg exch
neg exch translate
 440 834
a 440 822 a
currentpoint currentpoint translate 0 neg 5594038 atan rotate neg exch
neg exch translate
 440 822 a 378 812 a FB(H)s FF(\()p FB(z)r(;)7
b(t)p FF(\))440 834 y
grestore
 440 834 a 440 1189 a
gsave
 440 1189 a
440 1189 a
currentpoint currentpoint translate 0 neg 5594038 atan rotate neg exch
neg exch translate
 440 1189 a 259 1199 a Fw(\000)-17 b(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f
(\000)g(\000)g(\000)-17 b(\000)440 1189 y
grestore
 440 1189 a
440 1189 a
gsave
 440 1189 a 440 1189 a
currentpoint currentpoint translate 0 neg 5594038 atan rotate neg exch
neg exch translate
 440 1189 a 440 1201
a
currentpoint currentpoint translate 0 neg 5594038 atan rotate neg exch
neg exch translate
 440 1201 a 430 1220 a Fw(\003)440 1189 y
grestore
 440 1189 a
617 1012 a
gsave
 617 1012 a 617 1012 a
currentpoint currentpoint translate 5594036 neg 0 atan rotate neg exch
neg exch translate
 617 1012 a 436 1022
a Fw(\000)g(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h
(\000)f(\000)g(\000)g(\000)g(\000)g(\000)-16 b(\000)617
1012 y
grestore
 617 1012 a 440 923 a
gsave
 440 923 a 440 923 a
currentpoint currentpoint translate -2797018 neg 5594038 atan rotate
neg exch neg exch translate
 440 923
a 238 933 a Fw(\000)d(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)
-19 b(\000)440 923 y
grestore
 440 923 a 440 923 a
gsave
 440 923 a 440
923 a
currentpoint currentpoint translate -2797018 neg 5594038 atan rotate
neg exch neg exch translate
 440 923 a 300 967 a FB(H)s FF(\()p FB(z)r(;)7 b
FF(0\))k(=)h FB(f)t FF(\()p FB(z)r(;)7 b FF(1\))440 923
y
grestore
 440 923 a 784 1022 a FB(H)822 1005 y Fs(0)833 1022
y FF(\()p FB(z)r(;)g(t;)g(s)p FF(\))k(=)1013 937 y Fq(8)1013
974 y(<)1013 1049 y(:)1057 972 y FB(f)t FF(\()p FB(z)r(;)c
FF(2)p FB(s=)p FF(\(2)j Fw(\000)f FB(t)p FF(\)\))53 b(if)13
b(0)e Fw(\024)h FF(2)p FB(s)g Fw(\024)f FF(2)e Fw(\000)h
FB(t)1057 1072 y(H)s FF(\()p FB(z)r(;)d FF(2)p FB(s)i
Fw(\000)h FF(2)f(+)g FB(t)p FF(\))42 b(if)13 b(2)c Fw(\000)g
FB(t)j Fw(\024)g FF(2)p FB(s)f Fw(\024)h FF(2)-79 1471
y Fr(1)62 b Fx($$)-79 1520 y Fr(2)g Fx(\\def\\mod{\\)o(ma)o(thr)o(el)o
({\\b)o(ig/)o(}})-79 1570 y Fr(3)g Fx(\\Dg)-79 1620 y
Fr(4)g Fx({\\rm)18 b(Spin}\(3\))f(&)156 b(&)137 b(&)g(&)19
b(SU\(2\))136 b(\\\\)-79 1670 y Fr(5)337 b Fx(&)19 b(\\rdTo)37
b(&)137 b(&)19 b(\\ldTo)293 b(\\\\)-79 1720 y Fr(6)337
b Fx(&)156 b(&)19 b(SO\(3\))450 b(\\\\)-79 1769 y Fr(7)337
b Fx(&)156 b(&)19 b(\\dTo)470 b(\\\\)-79 1819 y Fr(8)62
b Fx(&)19 b(O\(3\)\\mod)e(O\(1\)^3)g(=)i({})g(&)g(SO\(3\)\\mod\()o
(O\(1)o(\)^3)o(\\c)o(ap)d(SO\(3\)\))i(\\\\)-79 1869 y
Fr(9)62 b Fx(\\endDg)-95 1919 y Fr(10)f Fx($$)1030 2150
y
gsave
 1030 2150 a 1030 2150 a
currentpoint currentpoint translate -2983488 neg 2797019 atan rotate
neg exch neg exch translate
 1030 2150 a 937 2161 a Fw(\000)-18
b(\000)-9 b(\000)g(\000)g(\000)h(\000)f(\000)-18 b Fv(\021)1030
2150 y
grestore
 1030 2150 a 1207 2150 a
gsave
 1207 2150 a 1207 2150
a
currentpoint currentpoint translate -2983488 neg -2797019 atan rotate
neg exch neg exch translate
 1207 2150 a 1114 2161 a Fw(\000)g(\000)-8 b(\000)f(\000)g(\000)g
(\000)g(\000)-17 b Fv(\021)1207 2150 y
grestore
 1207 2150 a 1119
2339 a
gsave
 1119 2339 a 1119 2339 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1119 2339 a 1053 2350
a Fw(\000)k(\000)k(\000)g(\000)d Fv(\021)1119 2339 y
grestore

1119 2339 a 875 2066 a FF(Spin)o(\(3\))231 b FB(S)r(U)5
b FF(\(2\))1062 2255 y FB(S)r(O)q FF(\(3\))597 2444 y
FB(O)q FF(\(3\))695 2411 y Fq(\016)730 2444 y FB(O)q
FF(\(1\))816 2427 y Fr(3)846 2444 y FF(=)12 b FB(S)r(O)q
FF(\(3\))1015 2411 y Fq(\016)1051 2444 y FF(\()p FB(O)q
FF(\(1\))1153 2427 y Fr(3)1181 2444 y Fw(\\)d FB(S)r(O)q
FF(\(3\)\))954 2770 y(58)p eop
%%Page: 59 3
59 58 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)0 42 y FH(S.)16 b(Mac)g(Lane)p
FF(,)d FC(Cate)n(gories)h(for)g(the)h(Working)h(Mathematician)p
FF(,)e(page)g(109.)-79 133 y Fr(1)62 b Fx($$)-79 183
y Fr(2)g Fx(\\def\\cod{{)o(\\r)o(m)17 b(cod}\\,})g(\\def\\dom)o({{\\)o
(rm)f(dom}\\,})-79 232 y Fr(3)62 b Fx(\\cellwidth)o(+=)o(2mm)-79
282 y Fr(4)g Fx(\\Dg)-79 332 y Fr(5)g Fx(&)19 b(F)g(&)h(_{\\cod)d(u})i
(&)g(\\rEq)136 b(&)19 b(F)g(&)g(_{\\cod)f(u})h(&)97 b(&)255
b(&)19 b(F_i)293 b(\\\\)-79 382 y Fr(6)62 b Fx(&)19 b(\\uTo)f(>{p_u})g
(&)h(&)235 b(&)19 b(\\uTo)f(&)157 b(&)97 b(&)20 b(\\ruTo)d(<{p_i})h
(\\tx{-5pt)o(})f(&)-79 432 y Fr(7)1376 b Fx(\\uDashto)17
b(>{\\mu_i})f(\\\\)-79 482 y Fr(8)62 b Fx({\\mit\\Pi}_)o({u)o(:j\\)o
(to)16 b(k}F_k)i(=)h({\\mit\\Pi})o(_u)d(&)-79 531 y Fr(9)101
b Fx(F)19 b(&)h(_{\\cod)d(u})i(&)g(\\lTo)f(^f)h(\\up{3pt})d(\\lTo)j(_g)
f(\\up{-3pt})-95 581 y Fr(10)630 b Fx(&)19 b({\\mit\\Pi}_)o(i)d(&)k(&)f
(F_i)f(&)i(\\lDashto)c(^e)j(&)g(d)333 b(\\\\)-95 631
y Fr(11)61 b Fx(&)19 b(\\dTo)f(>{p_u})g(&)h(&)235 b(&)19
b(\\dTo)f(>{p_{\\dom)e(u}})705 b(\\\\)-95 681 y Fr(12)61
b Fx(&)19 b(F)g(&)h(_{\\cod)d(u})i(&)g(\\lTo)f(^{Fu})g(&)h(F)g(&)g
(_{\\dom)f(u})803 b(\\\\)-95 731 y Fr(13)61 b Fx(\\endDg)-95
780 y Fr(14)g Fx($$)1018 915 y
gsave
 1018 915 a 1018 915 a
currentpoint currentpoint translate 0 neg 3793467 atan rotate neg exch
neg exch translate

1018 915 a 1013 925 a FF(=)1018 915 y
grestore
 1018 915 a 842
1009 a
gsave
 842 1009 a 842 1009 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 842 1009 a 774 1019 a Fw(\000)-15
b(\000)-9 b(\000)g(\000)g(\000)-15 b Fv(\021)842 1009
y
grestore
 842 1009 a 842 1009 a
gsave
 842 1009 a 842 1009 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 842 1009
a 846 1022 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 846 1022 a 10 x Fu(p)863 1036 y Fe(u)846
1009 y
grestore
 846 1009 a 1138 1009 a
gsave
 1138 1009 a 1138 1009 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate

1138 1009 a 1070 1019 a Fw(\000)f(\000)-9 b(\000)g(\000)g(\000)-15
b Fv(\021)1138 1009 y
grestore
 1138 1009 a 1276 1009 a
gsave
 1276 1009
a 1276 1009 a
currentpoint currentpoint translate 2983488 neg 3615060 atan rotate
neg exch neg exch translate
 1276 1009 a 1164 1019 a Fw(\000)-21 b(\000)-9
b(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)-20
b Fv(\021)1276 1009 y
grestore
 1276 1009 a 1276 1009 a
gsave
 1276 1009
a 1276 1009 a
currentpoint currentpoint translate 2983488 neg 3615060 atan rotate
neg exch neg exch translate
 1276 1009 a 1277 997 a
currentpoint currentpoint translate -2983488 neg 3615060 atan rotate
neg exch neg exch translate
 1277 997 a 1247
991 a Fu(p)1264 995 y Fe(i)1277 1009 y
grestore
 1277 1009 a 1391
1009 a
gsave
 1391 1009 a 1391 1009 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 1391 1009 a 1327 1019
a Fv(\013)-9 b(\013)g(\013)g(\013)g(\013)-14 b(\014)1391
1009 y
grestore
 1391 1009 a 1391 1009 a
gsave
 1391 1009 a 1391 1009
a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 1391 1009 a 1392 1022 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1392 1022 a 10 x Fu(\026)1412
1036 y Fe(i)1392 1009 y
grestore
 1392 1009 a 1018 1091 a
gsave
 1018
1091 a 1018 1091 a
currentpoint currentpoint translate 0 neg -3793467 atan rotate neg
exch neg exch translate
 1018 1091 a 930 1102 a Fw(\000)-19
b(\000)-9 b(\000)g(\000)g(\000)g(\000)-18 b Fv(\021)1018
1091 y
grestore
 1018 1091 a 1018 1091 a
gsave
 1018 1091 a 1018 1091
a
currentpoint currentpoint translate 0 neg -3793467 atan rotate neg
exch neg exch translate
 1018 1091 a 1011 1104 a
currentpoint currentpoint translate 0 neg -3793467 atan rotate neg
exch neg exch translate
 1011 1104 a 1001 1098 a Fu(f)1011
1091 y
grestore
 1011 1091 a 1018 1116 a
gsave
 1018 1116 a 1018 1116
a
currentpoint currentpoint translate 0 neg -3793467 atan rotate neg
exch neg exch translate
 1018 1116 a 930 1126 a Fw(\000)f(\000)-9 b(\000)g(\000)g(\000)g(\000)
-18 b Fv(\021)1018 1116 y
grestore
 1018 1116 a 1018 1116 a
gsave
 1018
1116 a 1018 1116 a
currentpoint currentpoint translate 0 neg -3793467 atan rotate neg
exch neg exch translate
 1018 1116 a 1011 1104 a
currentpoint currentpoint translate 0 neg -3793467 atan rotate neg
exch neg exch translate
 1011 1104
a 1002 1116 a Fu(g)1011 1116 y
grestore
 1011 1116 a 1286 1104
a
gsave
 1286 1104 a 1286 1104 a
currentpoint currentpoint translate 0 neg -3287380 atan rotate neg
exch neg exch translate
 1286 1104 a 1205 1114 a Fv(\013)-9
b(\013)g(\013)g(\013)h(\013)f(\013)-14 b(\014)1286 1104
y
grestore
 1286 1104 a 1286 1104 a
gsave
 1286 1104 a 1286 1104 a
currentpoint currentpoint translate 0 neg -3287380 atan rotate neg
exch neg exch translate
 1286
1104 a 1281 1116 a
currentpoint currentpoint translate 0 neg -3287380 atan rotate neg
exch neg exch translate
 1281 1116 a -8 w Fu(e)1281 1104 y
grestore

1281 1104 a 842 1198 a
gsave
 842 1198 a 842 1198 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 842 1198
a 767 1208 a Fw(\000)e(\000)-9 b(\000)g(\000)g(\000)-15
b Fv(\021)842 1198 y
grestore
 842 1198 a 842 1198 a
gsave
 842 1198 a
842 1198 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 842 1198 a 838 1186 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 838 1186 a 10 x Fu(p)855
1200 y Fe(u)838 1198 y
grestore
 838 1198 a 1138 1198 a
gsave
 1138 1198
a 1138 1198 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1138 1198 a 1068 1208 a Fw(\000)d(\000)-9
b(\000)g(\000)g(\000)-18 b Fv(\021)1138 1198 y
grestore
 1138 1198
a 1138 1198 a
gsave
 1138 1198 a 1138 1198 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1138 1198 a 1137
1186 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 1137 1186 a 10 x Fu(p)1154 1200 y Fp(dom)t Fe(u)1137
1198 y
grestore
 1137 1198 a 1018 1293 a
gsave
 1018 1293 a 1018 1293
a
currentpoint currentpoint translate 0 neg -3793467 atan rotate neg
exch neg exch translate
 1018 1293 a 922 1303 a Fw(\000)j(\000)-9 b(\000)g(\000)g(\000)g(\000)
-14 b Fv(\021)1018 1293 y
grestore
 1018 1293 a 1018 1293 a
gsave
 1018
1293 a 1018 1293 a
currentpoint currentpoint translate 0 neg -3793467 atan rotate neg
exch neg exch translate
 1018 1293 a 1007 1305 a
currentpoint currentpoint translate 0 neg -3793467 atan rotate neg
exch neg exch translate
 1007 1305
a -23 w Fu(F)t(u)1007 1293 y
grestore
 1007 1293 a 826 925 a FB(F)859
931 y Fr(co)q(d)5 b Fu(u)1122 925 y FB(F)1160 931 y Fr(co)q(d)g
Fu(u)1370 925 y FB(F)1397 931 y Fu(i)539 1114 y FB(\005)574
1120 y Fu(u)p Fr(:)p Fu(j)r Fh(\021)p Fu(k)668 1114 y
FB(F)695 1120 y Fu(k)726 1114 y FF(=)12 b FB(\005)805
1120 y Fu(u)826 1114 y FB(F)859 1120 y Fr(co)q(d)5 b
Fu(u)1114 1114 y FB(\005)1149 1120 y Fu(i)1162 1114 y
FB(F)1189 1120 y Fu(i)1380 1114 y FB(d)826 1303 y(F)859
1309 y Fr(co)q(d)g Fu(u)1122 1303 y FB(F)1154 1309 y
Fr(dom)h Fu(u)0 1670 y FH(S.)16 b(Mac)g(Lane)p FF(,)d
FC(Cate)n(gories)h(for)g(the)h(Working)h(Mathematician)p
FF(,)e(page)g(117.)-79 1761 y Fr(1)62 b Fx($$)-79 1811
y Fr(2)g Fx(\\Dg)-79 1861 y Fr(3)g Fx(u)215 b(&)20 b(\\rTo)e(^{e_1})56
b(&)19 b(v)137 b(&)20 b(&)f(\\rTo)f(\\up{3pt})e(^f)j(\\rTo)f
(\\up{-3pt})e(_g)j(&)g(d)79 b(\\\\)-79 1911 y Fr(4)62
b Fx(\\uDashto)17 b(>s)h(&)294 b(&)19 b(\\dTo)f(>e)h(&)373
b(&)352 b(&)19 b(\\uTo)g(\\\\)-79 1961 y Fr(5)62 b Fx(w)215
b(&)20 b(\\rTo)e(^{ee_1s})e(&)j(w)137 b(&)20 b({})e(=)i({\\mit\\Pi})o
(k_)o(i)d(&)i(\\rTo)253 b(&)19 b(k_i)39 b(\\\\)-79 2010
y Fr(6)62 b Fx(\\endDg)-79 2060 y Fr(7)g Fx($$)812 2195
y
gsave
 812 2195 a 812 2195 a
currentpoint currentpoint translate 0 neg 2910900 atan rotate neg exch
neg exch translate
 812 2195 a 740 2205 a Fw(\000)-15
b(\000)-9 b(\000)g(\000)g(\000)-14 b Fv(\021)812 2195
y
grestore
 812 2195 a 812 2195 a
gsave
 812 2195 a 812 2195 a
currentpoint currentpoint translate 0 neg 2910900 atan rotate neg exch
neg exch translate
 812 2195
a 813 2182 a
currentpoint currentpoint translate 0 neg 2910900 atan rotate neg exch
neg exch translate
 813 2182 a 797 2178 a Fu(e)813 2182 y Fp(1)813
2195 y
grestore
 813 2195 a 1066 2182 a
gsave
 1066 2182 a 1066 2182 a
currentpoint currentpoint translate 0 neg 5101974 atan rotate neg exch
neg exch translate

1066 2182 a 924 2193 a Fw(\000)f(\000)-9 b(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)h(\000)f(\000)g(\000)-14 b Fv(\021)1066
2182 y
grestore
 1066 2182 a 1066 2182 a
gsave
 1066 2182 a 1066 2182
a
currentpoint currentpoint translate 0 neg 5101974 atan rotate neg exch
neg exch translate
 1066 2182 a 1066 2170 a
currentpoint currentpoint translate 0 neg 5101974 atan rotate neg exch
neg exch translate
 1066 2170 a 1056 2164 a Fu(f)1066
2182 y
grestore
 1066 2182 a 1066 2207 a
gsave
 1066 2207 a 1066 2207
a
currentpoint currentpoint translate 0 neg 5101974 atan rotate neg exch
neg exch translate
 1066 2207 a 924 2218 a Fw(\000)f(\000)-9 b(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)h(\000)f(\000)g(\000)-14 b Fv(\021)1066
2207 y
grestore
 1066 2207 a 1066 2207 a
gsave
 1066 2207 a 1066 2207
a
currentpoint currentpoint translate 0 neg 5101974 atan rotate neg exch
neg exch translate
 1066 2207 a 1066 2220 a
currentpoint currentpoint translate 0 neg 5101974 atan rotate neg exch
neg exch translate
 1066 2220 a 1057 2232 a Fu(g)1066
2207 y
grestore
 1066 2207 a 720 2289 a
gsave
 720 2289 a 720 2289 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 720
2289 a 642 2300 a Fv(\013)-9 b(\013)g(\013)g(\013)g(\013)g(\013)-16
b(\014)720 2289 y
grestore
 720 2289 a 720 2289 a
gsave
 720 2289 a 720
2289 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 720 2289 a 719 2302 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 719 2302 a 10 x Fu(s)719
2289 y
grestore
 719 2289 a 904 2289 a
gsave
 904 2289 a 904 2289 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 904
2289 a 829 2300 a Fw(\000)-22 b(\000)-9 b(\000)g(\000)g(\000)g(\000)-21
b Fv(\021)904 2289 y
grestore
 904 2289 a 904 2289 a
gsave
 904 2289 a
904 2289 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 904 2289 a 905 2277 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate
 905 2277 a 10 x Fu(e)905
2289 y
grestore
 905 2289 a 1228 2289 a
gsave
 1228 2289 a 1228 2289 a
currentpoint currentpoint translate 2983488 neg 0 atan rotate neg exch
neg exch translate

1228 2289 a 1160 2300 a Fw(\000)-16 b(\000)-9 b(\000)g(\000)g(\000)-15
b Fv(\021)1228 2289 y
grestore
 1228 2289 a 812 2384 a
gsave
 812 2384
a 812 2384 a
currentpoint currentpoint translate 0 neg 2910900 atan rotate neg exch
neg exch translate
 812 2384 a 744 2394 a Fw(\000)c(\000)-9
b(\000)g(\000)g(\000)-19 b Fv(\021)812 2384 y
grestore
 812 2384
a 812 2384 a
gsave
 812 2384 a 812 2384 a
currentpoint currentpoint translate 0 neg 2910900 atan rotate neg exch
neg exch translate
 812 2384 a 812 2371
a
currentpoint currentpoint translate 0 neg 2910900 atan rotate neg exch
neg exch translate
 812 2371 a 780 2367 a Fu(ee)812 2371 y Fp(1)828 2367
y Fu(s)812 2384 y
grestore
 812 2384 a 1110 2384 a
gsave
 1110 2384 a
1110 2384 a
currentpoint currentpoint translate 0 neg 3719362 atan rotate neg exch
neg exch translate
 1110 2384 a 1065 2394 a Fw(\000)g(\000)-10
b(\000)i(\000)f(\000)-19 b Fv(\021)1110 2384 y
grestore
 1110 2384
a 708 2205 a FB(u)162 b(v)303 b(d)705 2394 y(w)154 b(w)20
b FF(=)12 b FB(\005)s(k)1043 2400 y Fu(i)1210 2394 y
FB(k)1232 2400 y Fu(i)954 2770 y FF(59)p eop
%%Page: 60 4
60 59 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)0 42 y FH(S.)16 b(Mac)g(Lane)g(and)f(I.)h
(Mo)q(erdijk)p FF(,)c FC(She)n(aves)k(In)f(Ge)n(ometry)g(and)g(L)n(o)n
(gic)p FF(,)f(page)f(232.)-79 133 y Fr(1)62 b Fx($$)-79
183 y Fr(2)g Fx(\\cellwidth)o(+=)o(3mm)-79 232 y Fr(3)g
Fx(\\Dg)-79 282 y Fr(4)g Fx(Y)117 b(&)20 b(\\rMono)d(^y)i(&)g(A)333
b(&)19 b(\\rLine)e(\\jh)i(&)g(\\stop)312 b(\\\\)-79 332
y Fr(5)62 b Fx(\\dEpi)37 b(&)216 b(&)19 b(\\dEpi)253
b(&)235 b(&)19 b(\\mx{-1cm})232 b(\\\\)-79 382 y Fr(6)62
b Fx(D)117 b(&)20 b(\\rMono)d(^d)i(&)g(i_A\(A\))233 b(&)i(&)19
b(\\dLine)e(>{\\eta_A})g(\\jn)h(\\\\)-79 432 y Fr(7)62
b Fx(\\dMono)17 b(&)216 b(&)19 b(\\dMono)939 b(\\\\)-79
482 y Fr(8)62 b Fx(X)117 b(&)20 b(\\rMono)d(_x)i(&)g(\\overline)o({i_)o
(A\()o(A\)})d(&)j(\\lTo)f(\\jt)58 b(&)19 b(\\stop)312
b(\\\\)-79 531 y Fr(9)62 b Fx(\\endDg)-95 581 y Fr(10)f
Fx($$)923 715 y
gsave
 923 715 a 923 715 a
currentpoint currentpoint translate 0 neg 4107633 atan rotate neg exch
neg exch translate
 923 715 a 818 726
a Fv(\016)-10 b Fw(\000)h(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-14
b Fv(\021)923 715 y
grestore
 923 715 a 923 715 a
gsave
 923 715 a 923
715 a
currentpoint currentpoint translate 0 neg 4107633 atan rotate neg exch
neg exch translate
 923 715 a 924 703 a
currentpoint currentpoint translate 0 neg 4107633 atan rotate neg exch
neg exch translate
 924 703 a 915 697 a Fu(y)924
715 y
grestore
 924 715 a 1115 715 a
gsave
 1115 715 a 1115 715 a
currentpoint currentpoint translate 0 neg 1945767 atan rotate neg exch
neg exch translate
 1115
715 a 1077 726 a Fw(\000)-20 b(\000)-9 b(\000)g(\000)-19
b(\000)1115 715 y
grestore
 1115 715 a 793 810 a
gsave
 793 810 a 793
810 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 793 810 a 717 820 a Fw(\000)j(\000)-9 b(\000)g(\000)g(\000)-15
b Fv(\021)-30 b(\014)793 810 y
grestore
 793 810 a 1053 810 a
gsave
 1053
810 a 1053 810 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1053 810 a 977 820 a Fw(\000)-17 b(\000)-9
b(\000)g(\000)g(\000)-16 b Fv(\021)-30 b(\014)1053 810
y
grestore
 1053 810 a 923 904 a
gsave
 923 904 a 923 904 a
currentpoint currentpoint translate 0 neg 4107633 atan rotate neg exch
neg exch translate
 923 904 a
819 915 a Fv(\016)-18 b Fw(\000)-9 b(\000)g(\000)h(\000)f(\000)g(\000)
-21 b Fv(\021)923 904 y
grestore
 923 904 a 923 904 a
gsave
 923 904 a
923 904 a
currentpoint currentpoint translate 0 neg 4107633 atan rotate neg exch
neg exch translate
 923 904 a 906 892 a
currentpoint currentpoint translate 0 neg 4107633 atan rotate neg exch
neg exch translate
 906 892 a -9 w Fu(d)906
904 y
grestore
 906 904 a 1176 904 a
gsave
 1176 904 a 1176 904 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 1176
904 a 983 915 a Fw(\000)k(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)h
(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-16
b(\000)1176 904 y
grestore
 1176 904 a 1176 904 a
gsave
 1176 904 a 1176
904 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 1176 904 a 1176 892 a
currentpoint currentpoint translate 5966976 neg 0 atan rotate neg exch
neg exch translate
 1176 892 a 10 x Fu(\021)1193
906 y Fe(A)1176 904 y
grestore
 1176 904 a 793 999 a
gsave
 793 999 a
793 999 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 793 999 a 717 1009 a Fv(\016)-9 b Fw(\000)g(\000)g(\000)g
(\000)c Fv(\021)793 999 y
grestore
 793 999 a 1053 999 a
gsave
 1053 999
a 1053 999 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1053 999 a 987 1009 a Fv(\016)-8 b Fw(\000)f(\000)g(\000)d
Fv(\021)1053 999 y
grestore
 1053 999 a 923 1093 a
gsave
 923 1093 a 923
1093 a
currentpoint currentpoint translate 0 neg 4107633 atan rotate neg exch
neg exch translate
 923 1093 a 820 1104 a Fv(\016)-18 b Fw(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)-22 b Fv(\021)923
1093 y
grestore
 923 1093 a 923 1093 a
gsave
 923 1093 a 923 1093 a
currentpoint currentpoint translate 0 neg 4107633 atan rotate neg exch
neg exch translate
 923
1093 a 906 1106 a
currentpoint currentpoint translate 0 neg 4107633 atan rotate neg exch
neg exch translate
 906 1106 a 897 1118 a Fu(x)906 1093
y
grestore
 906 1093 a 1115 1093 a
gsave
 1115 1093 a 1115 1093 a
currentpoint currentpoint translate 0 neg -1945767 atan rotate neg
exch neg exch translate
 1115
1093 a 1049 1104 a Fw(\000)i(\000)h Fv(\021)1115 1093
y
grestore
 1115 1093 a 776 726 a FB(Y)237 b(A)775 915 y(D)191
b(i)1014 921 y Fu(A)1042 915 y FF(\()p FB(A)p FF(\))774
1104 y FB(X)p 1000 1068 105 2 v 192 w(i)1014 1110 y Fu(A)1042
1104 y FF(\()p FB(A)p FF(\))0 1325 y FH(K.)17 b(S.)e(Bro)o(wn)p
FF(,)e FC(Cohomolo)n(gy)i(of)g(Gr)n(oups)p FF(,)e(page)h(280.)-79
1417 y Fr(1)62 b Fx($$)-79 1467 y Fr(2)g Fx(\\let\\^\\wid)o(eh)o(at)16
b(\\let\\~\\wid)o(eti)o(ld)o(e)-79 1516 y Fr(3)62 b Fx(\\flexible)16
b(\\columndis)o(t=1)o(cm)-79 1566 y Fr(4)62 b Fx(\\xgrid+=2m)o(m)16
b(\\ygrid+=-2m)o(m)-79 1616 y Fr(5)62 b Fx(\\Diagram)-79
1666 y Fr(6)219 b Fx(&)176 b(&)g(&)157 b(&H^0)18 b(\\bTo\(-1,-)o(4\))e
(\\hx{-2pt})-79 1716 y Fr(7)945 b Fx(&\\cdots)36 b(&H^{n-1})g(&H^n)i
(&H^{n+1})e(&H^{n+2})17 b(&\\cdots)g(\\\\)-79 1765 y
Fr(8)62 b Fx(\\mx{5mm}&)173 b(&)j(&)157 b(&\\dTo)57 b(&)156
b(&\\dTo)96 b(&\\dEpi&\\dB)o(ar)75 b(&\\dBar)17 b(&\\mx{-2mm}\\)o(\\)
-79 1815 y Fr(9)62 b Fx(\\cdots)37 b(&\\^H^{-3})16 b(&\\^H^{-2})g
(&\\^H^{-1}&)o(\\^H)o(^0)36 b(&\\cdots)g(&\\^H^{n-1})o(&\\^)o(H^)o
(n&\\)o(^H)o(^{n)o(+1)o(}&\\)o(^H^)o({n)o(+2})o(&\\)o(cdo)o(ts\\)o(\\)
-95 1865 y Fr(10)218 b Fx(&\\dBar)76 b(&\\dBar)g(&\\dInto)37
b(&\\dTo)57 b(&)156 b(&\\dTo)18 b(\\dx{-2mm})546 b(\\\\)-95
1915 y Fr(11)61 b Fx(\\cdots)37 b(&\\~H_{n+2)o(}&\\)o(~H_)o({n)o(+1})o
(&\\)o(~H_)o(n)56 b(&\\~H_{n-1)o(}&)o(\\cd)o(ots)o(&\\)o(~H_)o(0)16
b(\\aTo\(1,4\))h(\\hx{-2pt)o(})331 b(\\\\)-95 1965 y
Fr(12)61 b Fx(\\endDiagra)o(m)-95 2014 y Fr(13)g Fx($$)752
2345 y
gsave
 752 2345 a 752 2345 a
currentpoint currentpoint translate 5966976 neg 2106542 atan rotate
neg exch neg exch translate
 752 2345 a 592 2356 a Fw(\000)-21
b(\000)-9 b(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)-20 b Fv(\021)752 2345 y
grestore
 752
2345 a 827 2251 a
gsave
 827 2251 a 827 2251 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 827 2251 a 752
2261 a Fw(\000)e(\000)-9 b(\000)g(\000)g(\000)-21 b Fv(\021)827
2251 y
grestore
 827 2251 a 1087 2251 a
gsave
 1087 2251 a 1087 2251 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate

1087 2251 a 1011 2261 a Fw(\000)g(\000)-9 b(\000)g(\000)g(\000)-21
b Fv(\021)1087 2251 y
grestore
 1087 2251 a 1229 2251 a
gsave
 1229 2251
a 1229 2251 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1229 2251 a 1153 2261 a Fw(\000)f(\000)-9
b(\000)g(\000)h(\000)-21 b Fv(\021)-30 b(\014)1229 2251
y
grestore
 1229 2251 a 1371 2251 a
gsave
 1371 2251 a 1371 2251 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1371
2251 a 1295 2261 a FF(=)-17 b(=)-9 b(=)g(=)g(=)-17 b(=)1371
2251 y
grestore
 1371 2251 a 1512 2251 a
gsave
 1512 2251 a 1512 2251
a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1512 2251 a 1437 2261 a FF(=)f(=)-9 b(=)h(=)f(=)-17
b(=)1512 2251 y
grestore
 1512 2251 a 402 2440 a
gsave
 402 2440 a 402
2440 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 402 2440 a 326 2450 a FF(=)g(=)-9 b(=)g(=)g(=)-16
b(=)402 2440 y
grestore
 402 2440 a 544 2440 a
gsave
 544 2440 a 544 2440
a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 544 2440 a 468 2450 a FF(=)f(=)-9 b(=)g(=)g(=)-16 b(=)544
2440 y
grestore
 544 2440 a 686 2440 a
gsave
 686 2440 a 686 2440 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 686
2440 a 610 2450 a FB(,)-7 b Fw(\000)-13 b(\000)k(\000)g(\000)d
Fv(\021)686 2440 y
grestore
 686 2440 a 827 2440 a
gsave
 827 2440 a 827
2440 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 827 2440 a 752 2450 a Fw(\000)-22 b(\000)-9 b(\000)g(\000)g
(\000)-21 b Fv(\021)827 2440 y
grestore
 827 2440 a 1087 2440 a
gsave

1087 2440 a 1087 2440 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1087 2440 a 1011 2450 a Fw(\000)g(\000)-9
b(\000)g(\000)g(\000)-21 b Fv(\021)1087 2440 y
grestore
 1087 2440
a 1154 2345 a
gsave
 1154 2345 a 1154 2345 a
currentpoint currentpoint translate 5966976 neg 2106542 atan rotate
neg exch neg exch translate
 1154 2345 a 994
2356 a Fw(\000)g(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)h(\000)f(\000)-20 b Fv(\021)1154
2345 y
grestore
 1154 2345 a 799 2167 a FB(H)837 2149 y Fr(0)945
2167 y Fw(\001)7 b(\001)g(\001)41 b FB(H)1074 2149 y
Fu(n)p Fs(\000)p Fr(1)1199 2167 y FB(H)1237 2149 y Fu(n)1319
2167 y FB(H)1357 2149 y Fu(n)p Fr(+1)1461 2167 y FB(H)1499
2149 y Fu(n)p Fr(+2)1606 2167 y Fw(\001)7 b(\001)g(\001)295
2356 y(\001)g(\001)g(\001)371 2345 y Fq(b)361 2356 y
FB(H)399 2338 y Fs(\000)p Fr(3)512 2345 y Fq(b)503 2356
y FB(H)541 2338 y Fs(\000)p Fr(2)654 2345 y Fq(b)644
2356 y FB(H)682 2338 y Fs(\000)p Fr(1)809 2345 y Fq(b)799
2356 y FB(H)837 2338 y Fr(0)945 2356 y Fw(\001)g(\001)g(\001)1045
2345 y Fq(b)1036 2356 y FB(H)1074 2338 y Fu(n)p Fs(\000)p
Fr(1)1208 2345 y Fq(b)1199 2356 y FB(H)1237 2338 y Fu(n)1329
2345 y Fq(b)1319 2356 y FB(H)1357 2338 y Fu(n)p Fr(+1)1471
2345 y Fq(b)1461 2356 y FB(H)1499 2338 y Fu(n)p Fr(+2)1606
2356 y Fw(\001)g(\001)g(\001)295 2545 y(\001)g(\001)g(\001)362
2534 y Fq(e)353 2545 y FB(H)388 2551 y Fu(n)p Fr(+2)504
2534 y Fq(e)494 2545 y FB(H)529 2551 y Fu(n)p Fr(+1)667
2534 y Fq(e)657 2545 y FB(H)692 2551 y Fu(n)787 2534
y Fq(e)778 2545 y FB(H)813 2551 y Fu(n)p Fs(\000)p Fr(1)945
2545 y Fw(\001)g(\001)g(\001)1070 2534 y Fq(e)1061 2545
y FB(H)1096 2551 y Fr(0)954 2770 y FF(60)p eop
%%Page: 61 5
61 60 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)0 42 y FH(George)15 b(W.)h(Whitehead)p
FF(,)11 b FC(Elements)k(of)g(Homotopy)g(The)n(ory)p FF(,)e(page)h(592.)
-79 133 y Fr(1)62 b Fx($$)-79 183 y Fr(2)g Fx(\\def\\T{{\\b)o(f)16
b(T}})j(\\def\\S{{\\)o(bf)d(S}})-79 232 y Fr(3)62 b Fx(\\landscape)16
b(\\let\\labe)o(lst)o(yl)o(e\\t)o(ex)o(tst)o(yl)o(e)-79
282 y Fr(4)62 b Fx(\\cellpush=)o(10)o(pt)16 b(\\xscale=2.)o(2)-79
332 y Fr(5)62 b Fx(\\Diagram)-79 382 y Fr(6)199 b Fx(&)353
b(&)19 b(H_n\(X^+\\cu)o(p\\T)d(A^+,)i(X^+\))g(&)-79 432
y Fr(7)121 b Fx(\\lTo)18 b(^{H_n\(k_1)o(\)})e(&)157 b(&)19
b(H_n\(\\T)e(A^+,A^+\))-79 482 y Fr(8)670 b Fx(\\aTo)18
b(\(-3,-2\))f(_{H_n\(p_1\))o(})-79 531 y Fr(9)670 b Fx(\\aTo)18
b(\(3,-4\))f(^{\\partial_)o(1})369 b(\\\\)-95 581 y Fr(10)198
b Fx(&)353 b(&)19 b(\\dTo)f(>{H_n{q_1})o(})605 b(\\\\)-95
631 y Fr(11)198 b Fx(&)353 b(&)19 b(H_n\(\\S)e(A^+,P\))214
b(&)-95 681 y Fr(12)453 b Fx(&)157 b(&)19 b(*)g(\\dx{.7})684
b(\\\\)-95 731 y Fr(13)198 b Fx(&)20 b(\\ruTo)d(_{H_n\(q_4\))o(})g
(\\tx{15pt)o(})-95 780 y Fr(14)571 b Fx(&)19 b(\\uTo)f(>{H_n\(t\)})644
b(\\\\)-95 830 y Fr(15)61 b Fx(H_n\(X^+\\cu)o(p\\)o(T)17
b(A^+,P\))g(\\aTo)h(\(2,4\))37 b(^{H_n\(j_1\))o(})17
b(\\tx{15pt})-95 880 y Fr(16)473 b Fx(\\aTo)18 b(\(2,-4\))f
(_{H_n\(j_2\))o(})g(\\tx{15pt})-95 930 y Fr(17)198 b
Fx(&)59 b(&)f(&)78 b(&)157 b(&)58 b(&)19 b(H_{n-1}\(A\))d(&)-95
980 y Fr(18)787 b Fx(\\rTo)18 b(^{H_{n-1})o(\(i_)o(A\))o(})f(&)i
(H_{n-1}\(A)o(^+,)o(P\))d(\\\\)-95 1029 y Fr(19)198 b
Fx(&)20 b(\\rdTo)d(^{H_n\(q_2\))o(})g(\\tx{15pt)o(})-95
1079 y Fr(20)571 b Fx(&)490 b(&)19 b(&)g(&)h(\\ruTo)233
b(\\\\)-95 1129 y Fr(21)198 b Fx(&)353 b(&)19 b(H_n\(X^+/A^)o(+,P)o(\))
193 b(&)-95 1179 y Fr(22)100 b Fx(\\lTo)18 b(^{P_n\(X,A\))o(})36
b(&)20 b(H_n\(X,A\))-95 1229 y Fr(23)493 b Fx(\\aTo)18
b(\(1,-2\))f(>{H_n\(i_X)o(\)})585 b(\\\\)-95 1279 y Fr(24)198
b Fx(&)353 b(&)19 b(\\uTo)f(>{H_n\(q_3\))o(})605 b(\\\\)-95
1328 y Fr(25)198 b Fx(&)353 b(&)19 b(H_n\(X^+\\cu)o(p\\T)d(A^+,\\T)h
(A^+\)&)-95 1378 y Fr(26)100 b Fx(\\lTo)18 b(_{H_n\(k_2\))o(})f(&)i(&)g
(H_n\(X^+,A^)o(+\))-95 1428 y Fr(27)512 b Fx(\\aTo)18
b(\(3,4\))g(_{\\partia)o(l_2)o(})-95 1478 y Fr(28)512
b Fx(\\aTo)18 b(\(-3,2\))f(_{H_n\(p_X\)})565 b(\\\\)-95
1528 y Fr(29)61 b Fx(\\endDiagra)o(m)-95 1577 y Fr(30)g
Fx($$)954 2770 y FF(61)p eop
%%Page: 62 6
62 61 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)1491 2502 y
gsave
 1491 2502 a 1491
2502 a
currentpoint currentpoint translate 90 neg rotate neg exch neg exch
translate
 1491 2502 a 2593 1516 a
gsave
 2593 1516 a 2593 1516
a
currentpoint currentpoint translate 0 neg -12306864 atan rotate neg
exch neg exch translate
 2593 1516 a 2374 1526 a Fw(\000)-14 b(\000)-9 b(\000)h(\000)f(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)c
Fv(\021)2593 1516 y
grestore
 2593 1516 a 2593 1516 a
gsave
 2593 1516
a 2593 1516 a
currentpoint currentpoint translate 0 neg -12306864 atan rotate neg
exch neg exch translate
 2593 1516 a 2564 1528 a
currentpoint currentpoint translate 0 neg -12306864 atan rotate neg
exch neg exch translate
 2564 1528 a 2499
1518 a FB(H)2534 1524 y Fu(n)2556 1518 y FF(\()p FB(k)2594
1524 y Fr(1)2612 1518 y FF(\))2564 1516 y
grestore
 2564 1516 a
2593 1634 a
gsave
 2593 1634 a 2593 1634 a
currentpoint currentpoint translate -3729358 neg -12306864 atan rotate
neg exch neg exch translate
 2593 1634 a 2298
1644 a Fw(\000)-19 b(\000)-9 b(\000)g(\000)g(\000)g(\000)h(\000)f(\000)
g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)h(\000)f(\000)-19 b Fv(\021)2593
1634 y
grestore
 2593 1634 a 2593 1634 a
gsave
 2593 1634 a 2593 1634
a
currentpoint currentpoint translate -3729358 neg -12306864 atan rotate
neg exch neg exch translate
 2593 1634 a 2586 1622 a
currentpoint currentpoint translate 3729358 neg -12306864 atan rotate
neg exch neg exch translate
 2586 1622 a 31 x FB(H)2621
1659 y Fu(n)2643 1653 y FF(\()p FB(p)2680 1659 y Fr(1)2699
1653 y FF(\))2586 1634 y
grestore
 2586 1634 a 3281 1752 a
gsave
 3281
1752 a 3281 1752 a
currentpoint currentpoint translate -7458716 neg 9435275 atan rotate
neg exch neg exch translate
 3281 1752 a 2975 1763 a Fw(\000)k(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)-14 b Fv(\021)3281 1752 y
grestore
 3281 1752
a 3281 1752 a
gsave
 3281 1752 a 3281 1752 a
currentpoint currentpoint translate -7458716 neg 9435275 atan rotate
neg exch neg exch translate
 3281 1752 a 3278
1740 a
currentpoint currentpoint translate 7458716 neg 9435275 atan rotate
neg exch neg exch translate
 3278 1740 a -6 x FB(@)3300 1740 y Fr(1)3278 1752
y
grestore
 3278 1752 a 2203 1634 a
gsave
 2203 1634 a 2203 1634 a
currentpoint currentpoint translate -3729358 neg 0 atan rotate neg
exch neg exch translate
 2203
1634 a 2147 1644 a Fw(\000)-22 b(\000)-9 b(\000)g(\000)-22
b Fv(\021)2203 1634 y
grestore
 2203 1634 a 2203 1634 a
gsave
 2203 1634
a 2203 1634 a
currentpoint currentpoint translate -3729358 neg 0 atan rotate neg
exch neg exch translate
 2203 1634 a 2201 1622 a
currentpoint currentpoint translate 3729358 neg 0 atan rotate neg exch
neg exch translate
 2201 1622 a 10
x FB(H)2236 1638 y Fu(n)2258 1632 y FB(q)2277 1638 y
Fr(1)2201 1634 y
grestore
 2201 1634 a 1974 1870 a
gsave
 1974 1870 a
1974 1870 a
currentpoint currentpoint translate 3729358 neg 7221536 atan rotate
neg exch neg exch translate
 1974 1870 a 1812 1881 a Fw(\000)-13 b(\000)k(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)d
Fv(\021)1974 1870 y
grestore
 1974 1870 a 1974 1870 a
gsave
 1974 1870
a 1974 1870 a
currentpoint currentpoint translate 3729358 neg 7221536 atan rotate
neg exch neg exch translate
 1974 1870 a 1978 1883 a
currentpoint currentpoint translate -3729358 neg 7221536 atan rotate
neg exch neg exch translate
 1978 1883 a 31
x FB(H)2013 1920 y Fu(n)2036 1914 y FF(\()p FB(q)2071
1920 y Fr(4)2089 1914 y FF(\))1978 1870 y
grestore
 1978 1870 a
2203 1988 a
gsave
 2203 1988 a 2203 1988 a
currentpoint currentpoint translate 7458716 neg 0 atan rotate neg exch
neg exch translate
 2203 1988 a 2033
1999 a Fw(\000)-19 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-18 b Fv(\021)2203
1988 y
grestore
 2203 1988 a 2203 1988 a
gsave
 2203 1988 a 2203 1988
a
currentpoint currentpoint translate 7458716 neg 0 atan rotate neg exch
neg exch translate
 2203 1988 a 2205 2001 a
currentpoint currentpoint translate -7458716 neg 0 atan rotate neg
exch neg exch translate
 2205 2001 a 10 x FB(H)2240
2017 y Fu(n)2262 2011 y FF(\()p FB(t)p FF(\))2205 1988
y
grestore
 2205 1988 a 1974 1752 a
gsave
 1974 1752 a 1974 1752 a
currentpoint currentpoint translate 7458716 neg 7221536 atan rotate
neg exch neg exch translate
 1974
1752 a 1722 1763 a Fw(\000)h(\000)-9 b(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)-16 b Fv(\021)1974
1752 y
grestore
 1974 1752 a 1974 1752 a
gsave
 1974 1752 a 1974 1752
a
currentpoint currentpoint translate 7458716 neg 7221536 atan rotate
neg exch neg exch translate
 1974 1752 a 1977 1740 a
currentpoint currentpoint translate -7458716 neg 7221536 atan rotate
neg exch neg exch translate
 1977 1740 a 1852 1729 a FB(H)1887
1735 y Fu(n)1909 1729 y FF(\()p FB(j)1942 1735 y Fr(1)1961
1729 y FF(\))1977 1752 y
grestore
 1977 1752 a 1974 2225 a
gsave
 1974
2225 a 1974 2225 a
currentpoint currentpoint translate -7458716 neg 7221536 atan rotate
neg exch neg exch translate
 1974 2225 a 1716 2235 a Fw(\000)f(\000)-9
b(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)-16
b Fv(\021)1974 2225 y
grestore
 1974 2225 a 1974 2225 a
gsave
 1974 2225
a 1974 2225 a
currentpoint currentpoint translate -7458716 neg 7221536 atan rotate
neg exch neg exch translate
 1974 2225 a 1971 2237 a
currentpoint currentpoint translate 7458716 neg 7221536 atan rotate
neg exch neg exch translate
 1971 2237 a 1847
2268 a FB(H)1882 2274 y Fu(n)1904 2268 y FF(\()p FB(j)1937
2274 y Fr(2)1956 2268 y FF(\))1971 2225 y
grestore
 1971 2225 a
3320 1988 a
gsave
 3320 1988 a 3320 1988 a
currentpoint currentpoint translate 0 neg 8204576 atan rotate neg exch
neg exch translate
 3320 1988 a 3184
1999 a Fw(\000)f(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)-15 b Fv(\021)3320 1988 y
grestore
 3320 1988 a 3320 1988
a
gsave
 3320 1988 a 3320 1988 a
currentpoint currentpoint translate 0 neg 8204576 atan rotate neg exch
neg exch translate
 3320 1988 a 3300 1976 a
currentpoint currentpoint translate 0 neg 8204576 atan rotate neg exch
neg exch translate
 3300
1976 a 3214 1966 a FB(H)3249 1972 y Fu(n)p Fs(\000)p
Fr(1)3314 1966 y FF(\()p FB(i)3344 1972 y Fu(A)3371 1966
y FF(\))3300 1988 y
grestore
 3300 1988 a 1974 2106 a
gsave
 1974 2106
a 1974 2106 a
currentpoint currentpoint translate -3729358 neg 7221536 atan rotate
neg exch neg exch translate
 1974 2106 a 1804 2117 a Fw(\000)h(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g
(\000)c Fv(\021)1974 2106 y
grestore
 1974 2106 a 1974 2106 a
gsave
 1974
2106 a 1974 2106 a
currentpoint currentpoint translate -3729358 neg 7221536 atan rotate
neg exch neg exch translate
 1974 2106 a 1970 2094 a
currentpoint currentpoint translate 3729358 neg 7221536 atan rotate
neg exch neg exch translate
 1970 2094
a -10 x FB(H)2005 2090 y Fu(n)2027 2084 y FF(\()p FB(q)2062
2090 y Fr(2)2080 2084 y FF(\))1970 2106 y
grestore
 1970 2106 a
2892 2106 a
gsave
 2892 2106 a 2892 2106 a
currentpoint currentpoint translate 3729358 neg 5332987 atan rotate
neg exch neg exch translate
 2892 2106 a 2763
2117 a Fw(\000)c(\000)-9 b(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g
(\000)g(\000)-16 b Fv(\021)2892 2106 y
grestore
 2892 2106 a 2463
2225 a
gsave
 2463 2225 a 2463 2225 a
currentpoint currentpoint translate 0 neg -8204576 atan rotate neg
exch neg exch translate
 2463 2225 a 2332 2235
a Fw(\000)e(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-18
b Fv(\021)2463 2225 y
grestore
 2463 2225 a 2463 2225 a
gsave
 2463 2225
a 2463 2225 a
currentpoint currentpoint translate 0 neg -8204576 atan rotate neg
exch neg exch translate
 2463 2225 a 2436 2237 a
currentpoint currentpoint translate 0 neg -8204576 atan rotate neg
exch neg exch translate
 2436 2237 a 2353
2227 a FB(P)2380 2233 y Fu(n)2402 2227 y FF(\()p FB(X)q(;)7
b(A)p FF(\))2436 2225 y
grestore
 2436 2225 a 2853 2343 a
gsave
 2853
2343 a 2853 2343 a
currentpoint currentpoint translate -3729358 neg 4102288 atan rotate
neg exch neg exch translate
 2853 2343 a 2749 2353 a Fw(\000)-22
b(\000)-8 b(\000)f(\000)g(\000)g(\000)g(\000)g(\000)-21
b Fv(\021)2853 2343 y
grestore
 2853 2343 a 2853 2343 a
gsave
 2853 2343
a 2853 2343 a
currentpoint currentpoint translate -3729358 neg 4102288 atan rotate
neg exch neg exch translate
 2853 2343 a 2850 2330 a
currentpoint currentpoint translate 3729358 neg 4102288 atan rotate
neg exch neg exch translate
 2850 2330 a -10
x FB(H)2885 2326 y Fu(n)2907 2320 y FF(\()p FB(i)2937
2326 y Fu(X)2969 2320 y FF(\))2850 2343 y
grestore
 2850 2343 a
2203 2343 a
gsave
 2203 2343 a 2203 2343 a
currentpoint currentpoint translate 3729358 neg 0 atan rotate neg exch
neg exch translate
 2203 2343 a 2151
2353 a Fw(\000)f(\000)-9 b(\000)g(\000)-22 b Fv(\021)2203
2343 y
grestore
 2203 2343 a 2203 2343 a
gsave
 2203 2343 a 2203 2343
a
currentpoint currentpoint translate 3729358 neg 0 atan rotate neg exch
neg exch translate
 2203 2343 a 2205 2355 a
currentpoint currentpoint translate -3729358 neg 0 atan rotate neg
exch neg exch translate
 2205 2355 a 11 x FB(H)2240
2372 y Fu(n)2262 2366 y FF(\()p FB(q)2297 2372 y Fr(3)2316
2366 y FF(\))2205 2343 y
grestore
 2205 2343 a 2593 2461 a
gsave
 2593
2461 a 2593 2461 a
currentpoint currentpoint translate 0 neg -12306864 atan rotate neg
exch neg exch translate
 2593 2461 a 2361 2471 a Fw(\000)-14
b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f
(\000)g(\000)g(\000)g(\000)g(\000)c Fv(\021)2593 2461
y
grestore
 2593 2461 a 2593 2461 a
gsave
 2593 2461 a 2593 2461 a
currentpoint currentpoint translate 0 neg -12306864 atan rotate neg
exch neg exch translate
 2593
2461 a 2550 2448 a
currentpoint currentpoint translate 0 neg -12306864 atan rotate neg
exch neg exch translate
 2550 2448 a 2485 2479 a FB(H)2520
2485 y Fu(n)2542 2479 y FF(\()p FB(k)2580 2485 y Fr(2)2599
2479 y FF(\))2550 2461 y
grestore
 2550 2461 a 3281 2225 a
gsave
 3281
2225 a 3281 2225 a
currentpoint currentpoint translate 7458716 neg 9435275 atan rotate
neg exch neg exch translate
 3281 2225 a 2981 2235 a Fw(\000)e(\000)-9
b(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h
(\000)f(\000)g(\000)-14 b Fv(\021)3281 2225 y
grestore
 3281 2225
a 3281 2225 a
gsave
 3281 2225 a 3281 2225 a
currentpoint currentpoint translate 7458716 neg 9435275 atan rotate
neg exch neg exch translate
 3281 2225 a 3284
2237 a
currentpoint currentpoint translate -7458716 neg 9435275 atan rotate
neg exch neg exch translate
 3284 2237 a 29 x FB(@)3306 2272 y Fr(2)3284 2225
y
grestore
 3284 2225 a 2593 2343 a
gsave
 2593 2343 a 2593 2343 a
currentpoint currentpoint translate 3729358 neg -12306864 atan rotate
neg exch neg exch translate
 2593
2343 a 2312 2353 a Fw(\000)-19 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-18
b Fv(\021)2593 2343 y
grestore
 2593 2343 a 2593 2343 a
gsave
 2593 2343
a 2593 2343 a
currentpoint currentpoint translate 3729358 neg -12306864 atan rotate
neg exch neg exch translate
 2593 2343 a 2600 2330 a
currentpoint currentpoint translate -3729358 neg -12306864 atan rotate
neg exch neg exch translate
 2600 2330 a 2458
2361 a FB(H)2493 2367 y Fu(n)2515 2361 y FF(\()p FB(p)2552
2367 y Fu(X)2584 2361 y FF(\))2600 2343 y
grestore
 2600 2343 a
2015 1526 a FB(H)2050 1532 y Fu(n)2072 1526 y FF(\()p
FB(X)2125 1509 y Fr(+)2163 1526 y Fw([)9 b FH(T)p FB(A)2264
1509 y Fr(+)2291 1526 y FB(;)e(X)2347 1509 y Fr(+)2375
1526 y FF(\))462 b FB(H)2888 1532 y Fu(n)2911 1526 y
FF(\()p FH(T)p FB(A)2991 1509 y Fr(+)3019 1526 y FB(;)7
b(A)3069 1509 y Fr(+)3096 1526 y FF(\))2090 1763 y FB(H)2125
1769 y Fu(n)2147 1763 y FF(\()p FH(S)p FB(A)2221 1745
y Fr(+)2249 1763 y FB(;)g(P)f FF(\))655 b Fw(\003)1512
1999 y FB(H)1547 2005 y Fu(n)1569 1999 y FF(\()p FB(X)1622
1982 y Fr(+)1659 1999 y Fw([)9 b FH(T)p FB(A)1760 1982
y Fr(+)1788 1999 y FB(;)e(P)f FF(\))1123 b FB(H)3014
2005 y Fu(n)p Fs(\000)p Fr(1)3079 1999 y FF(\()p FB(A)p
FF(\))318 b FB(H)3495 2005 y Fu(n)p Fs(\000)p Fr(1)3559
1999 y FF(\()p FB(A)3606 1982 y Fr(+)3634 1999 y FB(;)7
b(P)f FF(\))2062 2235 y FB(H)2097 2241 y Fu(n)2119 2235
y FF(\()p FB(X)2172 2218 y Fr(+)2200 2235 y FB(=)n(A)2250
2218 y Fr(+)2277 2235 y FB(;)h(P)f FF(\))291 b FB(H)2671
2241 y Fu(n)2693 2235 y FF(\()p FB(X)q(;)7 b(A)p FF(\))2002
2471 y FB(H)2037 2477 y Fu(n)2059 2471 y FF(\()p FB(X)2112
2454 y Fr(+)2149 2471 y Fw([)i FH(T)p FB(A)2250 2454
y Fr(+)2278 2471 y FB(;)e FH(T)p FB(A)2361 2454 y Fr(+)2388
2471 y FF(\))463 b FB(H)2902 2477 y Fu(n)2924 2471 y
FF(\()p FB(X)2977 2454 y Fr(+)3005 2471 y FB(;)7 b(A)3055
2454 y Fr(+)3082 2471 y FF(\))1491 2502 y
grestore
 1491 2502 a
954 2770 a FF(62)p eop
%%Page: 63 7
63 62 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)0 42 y FH(J.)16 b(McCleary)p
FF(,)d FC(A)i(User's)f(to)h(Sp)n(e)n(ctr)n(al)f(Se)n(quenc)n(es)p
FF(,)h(page)f(13.)-79 133 y Fr(1)62 b Fx($$)-79 183 y
Fr(2)g Fx(\\dotted)-79 232 y Fr(3)g Fx(\\grid=7mm)-79
282 y Fr(4)g Fx(\\yscale=2)-79 332 y Fr(5)g Fx(\\Diagram)-79
382 y Fr(6)g Fx(&&&&&&&&&x)o(z&)o(&&&)o(xy)o(z&&)o(&&x)o(y^)o(2z&)o(&&)
o(&xy)o(^3)o(z&\\)o(\\)-79 432 y Fr(7)g Fx(\\\\)-79 482
y Fr(8)g Fx(z&&&&zy&&&)o(&z)o(y^2)o(&&)o(&&z)o(y^3)o(\\\\)-79
531 y Fr(9)g Fx(\\dy{-.2})-95 581 y Fr(10)f Fx(&&&&&&&&&x)o(&&)o(&&x)o
(y&)o(&&&)o(xy^)o(2&)o(&&&)o(xy)o(^3\\)o(\\)-95 631 y
Fr(11)g Fx(\\\\)-95 681 y Fr(12)g Fx(&&&&y&&&&y)o(^2)o(&&&)o(&y)o(^3\\)
o(\\)-95 731 y Fr(13)g Fx(\\Modify)-95 780 y Fr(14)g
Fx(\\Line)18 b(\(0,0\))f(\(4,0\))h(\\dt{1pt})-95 830
y Fr(15)61 b Fx(\\Line)18 b(\(4,0\))f(\(8,0\))-95 880
y Fr(16)61 b Fx(\\Line)18 b(\(8,0\))f(\(12,0\))-95 930
y Fr(17)61 b Fx(\\Line)18 b(\(12,0\))f(\(22.5,0\))-95
980 y Fr(18)61 b Fx(\\Line)18 b(\(0,0\))f(\(0,3\))h(\\dt{1pt})-95
1029 y Fr(19)61 b Fx(\\Line)18 b(\(0,3\))f(\(0,5.2\))-95
1079 y Fr(20)61 b Fx(\\To)18 b(\(9,2\))g(\(12,0\))-95
1129 y Fr(21)61 b Fx(\\To)18 b(\(9,5\))g(\(12,3\))-95
1179 y Fr(22)61 b Fx(\\endDiagra)o(m)-95 1229 y Fr(23)g
Fx($$)772 1431 y FB(xz)277 b(xy)q(z)257 b(xy)1458 1413
y Fr(2)1477 1431 y FB(z)248 b(xy)1789 1413 y Fr(3)1808
1431 y FB(z)40 1761 y(z)300 b(z)r(y)281 b(z)r(y)723 1744
y Fr(2)1011 1761 y FB(z)r(y)1053 1744 y Fr(3)782 1960
y FB(x)296 b(xy)278 b(xy)1469 1943 y Fr(2)1754 1960 y
FB(xy)1799 1943 y Fr(3)370 2290 y FB(y)301 b(y)712 2273
y Fr(2)1022 2290 y FB(y)1043 2273 y Fr(3)40 1431 y Fw(\017)61
b(\017)h(\017)g(\017)f(\017)h(\017)g(\017)g(\017)f(\017)145
b(\017)61 b(\017)h(\017)144 b(\017)62 b(\017)g(\017)144
b(\017)62 b(\017)f(\017)145 b(\017)40 1596 y(\017)61
b(\017)h(\017)g(\017)f(\017)h(\017)g(\017)g(\017)f(\017)h(\017)g(\017)f
(\017)h(\017)g(\017)f(\017)h(\017)g(\017)f(\017)h(\017)g(\017)f(\017)h
(\017)g(\017)122 1761 y(\017)g(\017)g(\017)144 b(\017)62
b(\017)g(\017)144 b(\017)62 b(\017)f(\017)145 b(\017)61
b(\017)h(\017)g(\017)f(\017)h(\017)g(\017)f(\017)h(\017)g(\017)40
1960 y(\017)f(\017)h(\017)g(\017)f(\017)h(\017)g(\017)g(\017)f(\017)145
b(\017)61 b(\017)h(\017)144 b(\017)62 b(\017)g(\017)144
b(\017)62 b(\017)f(\017)145 b(\017)40 2125 y(\017)61
b(\017)h(\017)g(\017)f(\017)h(\017)g(\017)g(\017)f(\017)h(\017)g(\017)f
(\017)h(\017)g(\017)f(\017)h(\017)g(\017)f(\017)h(\017)g(\017)f(\017)h
(\017)g(\017)40 2290 y(\017)f(\017)h(\017)g(\017)144
b(\017)62 b(\017)g(\017)144 b(\017)62 b(\017)f(\017)145
b(\017)61 b(\017)h(\017)g(\017)f(\017)h(\017)g(\017)f(\017)h(\017)g
(\017)216 2280 y
gsave
 216 2280 a 216 2280 a
currentpoint currentpoint translate 0 neg 5221100 atan rotate neg exch
neg exch translate
 216 2280 a 46
2290 a Fw(\000)-18 b(\000)-8 b(\000)f(\000)g(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)g(\000)-17 b(\000)216 2280
y
grestore
 216 2280 a 546 2280 a
gsave
 546 2280 a 546 2280 a
currentpoint currentpoint translate 0 neg 5221100 atan rotate neg exch
neg exch translate
 546 2280
a 400 2290 a Fw(\000)-22 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)-22 b(\000)546 2280
y
grestore
 546 2280 a 877 2280 a
gsave
 877 2280 a 877 2280 a
currentpoint currentpoint translate 0 neg 5221100 atan rotate neg exch
neg exch translate
 877 2280
a 740 2290 a Fw(\000)-15 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)-15 b(\000)877 2280 y
grestore
 877
2280 a 1476 2280 a
gsave
 1476 2280 a 1476 2280 a
currentpoint currentpoint translate 0 neg 13705387 atan rotate neg
exch neg exch translate
 1476 2280
a 1071 2290 a Fw(\000)-21 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-20
b(\000)1476 2280 y
grestore
 1476 2280 a 50 2016 a
gsave
 50 2016 a 50
2016 a
currentpoint currentpoint translate 8353752 neg 0 atan rotate neg exch
neg exch translate
 50 2016 a -219 2026 a Fw(\000)f(\000)-9 b(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)-21 b(\000)50
2016 y
grestore
 50 2016 a 50 1569 a
gsave
 50 1569 a 50 1569 a
currentpoint currentpoint translate 5743202 neg 0 atan rotate neg exch
neg exch translate
 50 1569
a -116 1579 a Fw(\000)-13 b(\000)k(\000)g(\000)g(\000)g(\000)g(\000)h
(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)d(\000)50
1569 y
grestore
 50 1569 a 918 2115 a
gsave
 918 2115 a 918 2115 a
currentpoint currentpoint translate -5221100 neg 3915825 atan rotate
neg exch neg exch translate
 918
2115 a 733 2125 a Fw(\000)c(\000)-9 b(\000)h(\000)f(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-14
b Fv(\021)918 2115 y
grestore
 918 2115 a 918 1586 a
gsave
 918 1586 a
918 1586 a
currentpoint currentpoint translate -5221100 neg 3915825 atan rotate
neg exch neg exch translate
 918 1586 a 733 1596 a Fw(\000)e(\000)-9 b(\000)h(\000)f
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)
-14 b Fv(\021)918 1586 y
grestore
 918 1586 a 954 2770 a FF(63)p
eop
%%Page: 64 8
64 63 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)0 42 y FH(J.)16 b(McCleary)p
FF(,)d FC(A)i(User's)f(to)h(Sp)n(e)n(ctr)n(al)f(Se)n(quenc)n(es)p
FF(,)h(page)f(346.)-79 133 y Fr(1)62 b Fx($$)-79 183
y Fr(2)g Fx(\\cellpush+)o(=5)o(pt)-79 232 y Fr(3)g Fx(\\cellwidth)o(+=)
o(2mm)-79 282 y Fr(4)g Fx(\\Dg)-79 332 y Fr(5)g Fx(&&_{N+t'}X)o(_p)36
b(&)19 b(\\rTo)f(^{g_{p+q})o(})f(&)i(_N)g(X_{p+q})36
b(\\\\)-79 382 y Fr(6)62 b Fx(&&)19 b(\\dFillcel)o(l{\\)o(;\\)o(cdo)o
(ts\\)o(;\\)o(rig)o(ht)o(arr)o(ow)o(fil)o(l})d(&)-79
432 y Fr(7)690 b Fx(&)19 b(\\dFillcel)o(l{\\)o(;\\)o(cdo)o(ts\\)o(;\\)o
(rig)o(ht)o(arr)o(owf)o(il)o(l})d(\\\\)-79 482 y Fr(8)964
b Fx(\\\\)-79 531 y Fr(9)62 b Fx(&&)19 b(_{N+t'}X_)o(1)e(&)i(\\rTo)f
(^{g_{q+1})o(})f(&)i(_N)g(X_{q+1})36 b(\\\\)-95 581 y
Fr(10)61 b Fx(&&)19 b(\\dTo)136 b(&)333 b(&)19 b(\\dTo)155
b(\\\\)-95 631 y Fr(11)61 b Fx(S^{N+t+t'})o(X)16 b(\\aTo)i(\(2,5\))g
(^{f_p})f(\\tx{.7})g(\\hx{5pt})g(&)i(\\rTo)f(^f)h(&)-95
681 y Fr(12)120 b Fx(S^{N+t'}X)36 b(&)19 b(\\rTo)f(^{g_q})96
b(&)19 b(_N)g(X_q)116 b(\\\\)-95 731 y Fr(13)963 b Fx(\\\\)-95
780 y Fr(14)61 b Fx(&&)235 b(&)333 b(&)19 b(\\dFillcel)o(l{\\)o(ri)o
(ght)o(arr)o(ow)o(fil)o(l\\)o(;\\c)o(dot)o(s\\)o(;\\r)o(ig)o(hta)o(rr)o
(owf)o(ill)o(})d(\\\\)-95 830 y Fr(15)963 b Fx(\\\\)-95
880 y Fr(16)61 b Fx(&&)235 b(&)333 b(&)19 b(_N)g(X_1)116
b(\\\\)-95 930 y Fr(17)61 b Fx(&&)235 b(&)333 b(&)19
b(\\dTo)155 b(\\\\)-95 980 y Fr(18)61 b Fx(&&)235 b(&)333
b(&)19 b(S^N)f(X)i(\\bTo)e(\(-2,6\))f(<g)i(\\hx{.2})e(\\\\)-95
1029 y Fr(19)61 b Fx(\\endDg)-95 1079 y Fr(20)g Fx($$)1161
1214 y
gsave
 1161 1214 a 1161 1214 a
currentpoint currentpoint translate 0 neg 4858239 atan rotate neg exch
neg exch translate
 1161 1214 a 1103 1224
a Fw(\000)-16 b(\000)-10 b(\000)h(\000)-16 b Fv(\021)1161
1214 y
grestore
 1161 1214 a 1161 1214 a
gsave
 1161 1214 a 1161 1214
a
currentpoint currentpoint translate 0 neg 4858239 atan rotate neg exch
neg exch translate
 1161 1214 a 1163 1201 a
currentpoint currentpoint translate 0 neg 4858239 atan rotate neg exch
neg exch translate
 1163 1201 a 1128 1193 a Fu(g)1144
1197 y Fe(p)p Fp(+)p Fe(q)1163 1214 y
grestore
 1163 1214 a 1007
1355 a
gsave
 1007 1355 a 1007 1355 a
currentpoint currentpoint translate -4475232 neg 0 atan rotate neg
exch neg exch translate
 1007 1355 a 928 1366 a
Fw(\001)7 b(\001)g(\001)17 b(\000)-23 b(\000)-9 b(\000)g(\000)-22
b Fv(\021)1007 1355 y
grestore
 1007 1355 a 1314 1355 a
gsave
 1314 1355
a 1314 1355 a
currentpoint currentpoint translate -4475232 neg 0 atan rotate neg
exch neg exch translate
 1314 1355 a 1236 1366 a Fw(\001)7 b(\001)g(\001)16
b(\000)-23 b(\000)-8 b(\000)f(\000)-22 b Fv(\021)1314
1355 y
grestore
 1314 1355 a 1161 1497 a
gsave
 1161 1497 a 1161 1497
a
currentpoint currentpoint translate 0 neg 4858239 atan rotate neg exch
neg exch translate
 1161 1497 a 1103 1507 a Fw(\000)-16 b(\000)-10 b(\000)h(\000)-15
b Fv(\021)1161 1497 y
grestore
 1161 1497 a 1161 1497 a
gsave
 1161 1497
a 1161 1497 a
currentpoint currentpoint translate 0 neg 4858239 atan rotate neg exch
neg exch translate
 1161 1497 a 1163 1485 a
currentpoint currentpoint translate 0 neg 4858239 atan rotate neg exch
neg exch translate
 1163 1485 a 1129
1476 a Fu(g)1145 1480 y Fe(q)q Fp(+1)1163 1497 y
grestore
 1163
1497 a 1007 1591 a
gsave
 1007 1591 a 1007 1591 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1007 1591
a 961 1602 a Fw(\000)i(\000)h Fv(\021)1007 1591 y
grestore
 1007
1591 a 1314 1591 a
gsave
 1314 1591 a 1314 1591 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1314 1591
a 1271 1602 a Fw(\000)-20 b(\000)-8 b(\000)-19 b Fv(\021)1314
1591 y
grestore
 1314 1591 a 864 1450 a
gsave
 864 1450 a 864 1450 a
currentpoint currentpoint translate 7458720 neg 5151710 atan rotate
neg exch neg exch translate
 864
1450 a 644 1460 a Fw(\000)-12 b(\000)j(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g
(\000)g(\000)e Fv(\021)864 1450 y
grestore
 864 1450 a 864 1450
a
gsave
 864 1450 a 864 1450 a
currentpoint currentpoint translate 7458720 neg 5151710 atan rotate
neg exch neg exch translate
 864 1450 a 869 1437 a
currentpoint currentpoint translate -7458720 neg 5151710 atan rotate
neg exch neg exch translate
 869 1437
a 835 1429 a Fu(f)851 1433 y Fe(p)869 1450 y
grestore
 869 1450
a 836 1686 a
gsave
 836 1686 a 836 1686 a
currentpoint currentpoint translate 0 neg 5405808 atan rotate neg exch
neg exch translate
 836 1686 a 785 1696
a Fw(\000)-16 b(\000)-9 b(\000)g(\000)-16 b Fv(\021)836
1686 y
grestore
 836 1686 a 836 1686 a
gsave
 836 1686 a 836 1686 a
currentpoint currentpoint translate 0 neg 5405808 atan rotate neg exch
neg exch translate
 836
1686 a 845 1673 a
currentpoint currentpoint translate 0 neg 5405808 atan rotate neg exch
neg exch translate
 845 1673 a 835 1667 a Fu(f)845 1686
y
grestore
 845 1686 a 1161 1686 a
gsave
 1161 1686 a 1161 1686 a
currentpoint currentpoint translate 0 neg 4858239 atan rotate neg exch
neg exch translate
 1161
1686 a 1109 1696 a Fw(\000)c(\000)-10 b(\000)h(\000)h(\000)-20
b Fv(\021)1161 1686 y
grestore
 1161 1686 a 1161 1686 a
gsave
 1161 1686
a 1161 1686 a
currentpoint currentpoint translate 0 neg 4858239 atan rotate neg exch
neg exch translate
 1161 1686 a 1176 1673 a
currentpoint currentpoint translate 0 neg 4858239 atan rotate neg exch
neg exch translate
 1176 1673 a 1160
1665 a Fu(g)1176 1669 y Fe(q)1176 1686 y
grestore
 1176 1686 a
1314 1875 a
gsave
 1314 1875 a 1314 1875 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 1314 1875 a 1177
1885 a Fw(\000)k(\000)-9 b(\000)-16 b Fv(\021)18 b Fw(\001)7
b(\001)g(\001)17 b(\000)-16 b(\000)-9 b(\000)-15 b Fv(\021)1314
1875 y
grestore
 1314 1875 a 1314 2158 a
gsave
 1314 2158 a 1314 2158
a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1314 2158 a 1266 2169 a Fw(\000)-22 b(\000)-8 b(\000)-20
b Fv(\021)1314 2158 y
grestore
 1314 2158 a 1146 1969 a
gsave
 1146 1969
a 1146 1969 a
currentpoint currentpoint translate -8950464 neg 4398909 atan rotate
neg exch neg exch translate
 1146 1969 a 871 1980 a Fw(\000)i(\000)-9
b(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)
-16 b Fv(\021)1146 1969 y
grestore
 1146 1969 a 1146 1969 a
gsave
 1146
1969 a 1146 1969 a
currentpoint currentpoint translate -8950464 neg 4398909 atan rotate
neg exch neg exch translate
 1146 1969 a 1137 1982 a
currentpoint currentpoint translate 8950464 neg 4398909 atan rotate
neg exch neg exch translate
 1137 1982
a 1120 1994 a Fu(g)1137 1969 y
grestore
 1137 1969 a 940 1230 a
Fu(N)s Fr(+)p Fu(t)1007 1222 y Ft(0)1020 1224 y FB(X)1054
1230 y Fu(p)180 b(N)1283 1224 y FB(X)1317 1230 y Fu(p)p
Fr(+)p Fu(q)940 1514 y(N)s Fr(+)p Fu(t)1007 1505 y Ft(0)1021
1507 y FB(X)1055 1513 y Fr(1)1251 1514 y Fu(N)1283 1507
y FB(X)1317 1513 y Fu(q)q Fr(+1)572 1696 y FB(S)599 1679
y Fu(N)s Fr(+)p Fu(t)p Fr(+)p Fu(t)704 1667 y Ft(0)719
1696 y FB(X)h(S)961 1679 y Fu(N)s Fr(+)p Fu(t)1028 1667
y Ft(0)1042 1696 y FB(X)1272 1703 y Fu(N)1304 1696 y
FB(X)1338 1702 y Fu(q)1272 2081 y(N)1304 2074 y FB(X)1338
2080 y Fr(1)1266 2263 y FB(S)1293 2246 y Fu(N)1325 2263
y FB(X)954 2770 y FF(64)p eop
%%Page: 65 9
65 64 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)0 42 y FH(P)l(.)16 b(J.)g(Hilton)d(and)j
(U.)f(Stamm)o(bac)o(h)p FF(,)d FC(A)i(Course)h(in)g(Homolo)n(gic)n(al)f
(A)o(lgebr)n(a)p FF(,)f(page)h(149.)-79 133 y Fr(1)62
b Fx($$)-79 183 y Fr(2)g Fx(\\let~\\tild)o(e)-79 232
y Fr(3)g Fx(\\cellwidth)o(+=)o(17m)o(m)16 b(\\columndist)o(+=)o(12m)o
(m)-79 282 y Fr(4)62 b Fx(\\gravitate)o(le)o(ft)-79 332
y Fr(5)g Fx(\\Dg)-79 382 y Fr(6)101 b Fx(&)118 b(&)19
b(K)254 b(&)20 b(\\rMono)95 b(&&)19 b(E_1^\\alpha)o(&)e(\\rEpi^{\\)o
(eta)o('}&)o(&)f(A')117 b(\\\\)-79 432 y Fr(7)101 b Fx(&)19
b(\\ldTo&)292 b(&)235 b(&&)215 b(&)118 b(&)19 b(\\ruBar)213
b(\\\\)-79 482 y Fr(8)62 b Fx(~K&)117 b(&)19 b(\\dBar\\rMo)o(no\\)o(br)
o(&)e(~E_1^\\al)o(pha)o(&&)f(\\dTo\\rEpi^)o({~\\)o(et)o(a'})o(\\b)o(r&)
-79 531 y Fr(9)1102 b Fx(A')430 b(\\\\)-95 581 y Fr(10)61
b Fx(\\dBar&)c(&)293 b(&)235 b(&&)215 b(&)118 b(&)78
b(&)19 b(\\dTo>\\alp)o(ha)d(\\\\)-95 631 y Fr(11)100
b Fx(&)118 b(&)19 b(K)254 b(&)20 b(\\rMono\\d)o(To\\)o(br&)o(&)c
(E_1\\ax{2mm})o(&)g(\\rEpi\\dTo\\b)o(r&)o(&)h(A)97 b(\\\\)-95
681 y Fr(12)j Fx(&)19 b(\\ldTo&)292 b(&)118 b(&)19 b(\\ldTo&)213
b(&)118 b(&)19 b(\\ldBar)213 b(\\\\)-95 731 y Fr(13)61
b Fx(~K&)117 b(&)19 b(\\rMono)154 b(&)20 b(~E_1)e(&)h(\\rEpi_{~\\)o
(eta)o(}&)55 b(&)20 b(A)450 b(\\\\)-95 780 y Fr(14)61
b Fx(\\endDg)-95 830 y Fr(15)g Fx($$)931 969 y
gsave
 931 969
a 931 969 a
currentpoint currentpoint translate 0 neg 6716225 atan rotate neg exch
neg exch translate
 931 969 a 746 980 a Fv(\016)-16 b Fw(\000)-9
b(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)-19 b Fv(\021)931 969 y
grestore
 931 969 a
1346 969 a
gsave
 1346 969 a 1346 969 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1346 969 a 1181 980
a Fw(\000)c(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)h(\000)f(\000)g(\000)g(\000)-22 b Fv(\021)-30 b(\014)1346
969 y
grestore
 1346 969 a 1346 969 a
gsave
 1346 969 a 1346 969 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1346
969 a 1349 957 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1349 957 a 1334 951 a Fu(\021)1352 939
y Ft(0)1349 969 y
grestore
 1349 969 a 559 1064 a
gsave
 559 1064 a 559
1064 a
currentpoint currentpoint translate -2983488 neg -5034634 atan rotate
neg exch neg exch translate
 559 1064 a 402 1074 a Fw(\000)-12 b(\000)j(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)d Fv(\021)559
1064 y
grestore
 559 1064 a 1377 1064 a
gsave
 1377 1064 a 1377 1064 a
currentpoint currentpoint translate 2983488 neg 5407569 atan rotate
neg exch neg exch translate

1377 1064 a 1214 1074 a FF(=)-23 b(=)-9 b(=)h(=)f(=)g(=)g(=)g(=)g(=)g
(=)g(=)g(=)g(=)g(=)-22 b(=)1377 1064 y
grestore
 1377 1064 a 719
1158 a
gsave
 719 1158 a 719 1158 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 719 1158 a 548 1169 a FF(=)i(=)-9
b(=)g(=)g(=)g(=)g(=)g(=)g(=)g(=)g(=)g(=)h(=)f(=)-20 b(=)719
1158 y
grestore
 719 1158 a 601 1158 a
gsave
 601 1158 a 601 1158 a
currentpoint currentpoint translate 0 neg 6343290 atan rotate neg exch
neg exch translate
 601
1158 a 400 1158 a
1 setgray
 400 1158 a 427 1169 338 21 v 601 1158
a
grestore
 601 1158 a 601 1158 a
gsave
 601 1158 a 601 1158 a
currentpoint currentpoint translate 0 neg 6343290 atan rotate neg exch
neg exch translate
 601 1158
a 427 1169 a Fv(\016)k Fw(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)h
(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-20 b
Fv(\021)601 1158 y
grestore
 601 1158 a 1144 1158 a
gsave
 1144 1158 a
1144 1158 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 1144 1158 a 984 1169 a Fw(\000)h(\000)-9
b(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)-18 b Fv(\021)1144 1158 y
grestore
 1144 1158 a 1003 1158
a
gsave
 1003 1158 a 1003 1158 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1003 1158 a 801 1158 a
1 setgray
 801
1158 a 838 1169 338 21 v 1003 1158 a
grestore
 1003 1158 a 1003
1158 a
gsave
 1003 1158 a 1003 1158 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1003 1158 a 838 1169 a
Fw(\000)-23 b(\000)-8 b(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)g(\000)-22 b Fv(\021)-30
b(\014)1003 1158 y
grestore
 1003 1158 a 1003 1158 a
gsave
 1003 1158
a 1003 1158 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1003 1158 a 1006 1146 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1006 1146 a 994
1140 a Fr(~)-20 b Fu(\021)1009 1128 y Ft(0)1007 1158
y
grestore
 1007 1158 a 400 1347 a
gsave
 400 1347 a 400 1347 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 400 1347
a 229 1358 a FF(=)-13 b(=)k(=)g(=)g(=)g(=)g(=)g(=)g(=)g(=)g(=)g(=)g(=)c
(=)400 1347 y
grestore
 400 1347 a 1548 1158 a
gsave
 1548 1158 a 1548
1158 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 1548 1158 a 1378 1169 a Fw(\000)f(\000)-9 b(\000)g(\000)g(\000)h
(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)c
Fv(\021)1548 1158 y
grestore
 1548 1158 a 1548 1158 a
gsave
 1548 1158
a 1548 1158 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 1548 1158 a 1544 1146 a
currentpoint currentpoint translate 5966976 neg 0 atan rotate neg exch
neg exch translate
 1544 1146 a 10
x Fu(\013)1544 1158 y
grestore
 1544 1158 a 931 1347 a
gsave
 931 1347
a 931 1347 a
currentpoint currentpoint translate 0 neg 6716225 atan rotate neg exch
neg exch translate
 931 1347 a 746 1358 a Fv(\016)f Fw(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)-17 b Fv(\021)931 1347 y
grestore
 931 1347
a 801 1347 a
gsave
 801 1347 a 801 1347 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 801 1347 a 612 1347
a
1 setgray
 612 1347 a 641 1358 313 21 v 801 1347 a
grestore
 801 1347 a
801 1347 a
gsave
 801 1347 a 801 1347 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 801 1347 a 641 1358
a Fw(\000)-12 b(\000)j(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)e Fv(\021)801 1347 y
grestore
 801 1347 a 1346
1347 a
gsave
 1346 1347 a 1346 1347 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1346 1347 a 1177 1358
a Fw(\000)-18 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)h(\000)f(\000)g(\000)g(\000)g(\000)-17 b Fv(\021)-30
b(\014)1346 1347 y
grestore
 1346 1347 a 1206 1347 a
gsave
 1206 1347
a 1206 1347 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 1206 1347 a 1017 1347 a
1 setgray
 1017 1347 a 1035
1358 333 21 v 1206 1347 a
grestore
 1206 1347 a 1206 1347 a
gsave
 1206
1347 a 1206 1347 a
currentpoint currentpoint translate -5966976 neg 0 atan rotate neg
exch neg exch translate
 1206 1347 a 1035 1358 a Fw(\000)-13
b(\000)k(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)d Fv(\021)1206 1347 y
grestore
 1206 1347 a 559 1442
a
gsave
 559 1442 a 559 1442 a
currentpoint currentpoint translate -2983488 neg -5034634 atan rotate
neg exch neg exch translate
 559 1442 a 402 1452 a Fw(\000)g(\000)j(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)d
Fv(\021)559 1442 y
grestore
 559 1442 a 973 1442 a
gsave
 973 1442 a 973
1442 a
currentpoint currentpoint translate -2983488 neg -5407569 atan rotate
neg exch neg exch translate
 973 1442 a 814 1452 a Fw(\000)-21 b(\000)-9 b(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-20
b Fv(\021)973 1442 y
grestore
 973 1442 a 1377 1442 a
gsave
 1377 1442
a 1377 1442 a
currentpoint currentpoint translate -2983488 neg -5407569 atan rotate
neg exch neg exch translate
 1377 1442 a 1207 1452 a FF(=)j(=)-9 b(=)g(=)g(=)g(=)g(=)g
(=)g(=)g(=)g(=)h(=)f(=)g(=)-17 b(=)1377 1442 y
grestore
 1377 1442
a 601 1536 a
gsave
 601 1536 a 601 1536 a
currentpoint currentpoint translate 0 neg 6343290 atan rotate neg exch
neg exch translate
 601 1536 a 427 1547
a Fv(\016)j Fw(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)h(\000)f(\000)g(\000)g(\000)-18 b Fv(\021)601
1536 y
grestore
 601 1536 a 1003 1536 a
gsave
 1003 1536 a 1003 1536 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate

1003 1536 a 834 1547 a Fw(\000)h(\000)-9 b(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-17
b Fv(\021)-30 b(\014)1003 1536 y
grestore
 1003 1536 a 1003 1536
a
gsave
 1003 1536 a 1003 1536 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1003 1536 a 1008 1549 a
currentpoint currentpoint translate 0 neg 6379245 atan rotate neg exch
neg exch translate
 1008
1549 a 1002 1568 a Fr(~)-20 b Fu(\021)1008 1536 y
grestore
 1008
1536 a 699 980 a FB(K)382 b(E)1149 963 y Fu(\013)1147
990 y Fr(1)1527 980 y FB(A)1558 963 y Fs(0)392 1158 y
FF(~)381 1169 y FB(K)783 1158 y FF(~)773 1169 y FB(E)806
1152 y Fu(\013)804 1179 y Fr(1)1184 1169 y FB(A)1215
1152 y Fs(0)699 1358 y FB(K)j(E)1150 1364 y Fr(1)1532
1358 y FB(A)392 1536 y FF(~)381 1547 y FB(K)786 1536
y FF(~)777 1547 y FB(E)808 1553 y Fr(1)1190 1547 y FB(A)954
2770 y FF(65)p eop
%%Page: 66 10
66 65 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)0 42 y FH(George)15 b(W.)h(Whitehead)p
FF(,)11 b FC(Elements)k(of)g(Homotopy)g(The)n(ory)p FF(,)e(page)h(650.)
-79 133 y Fr(1)62 b Fx($$)-79 183 y Fr(2)g Fx(\\cellpush=)o(4p)o(t)-79
232 y Fr(3)g Fx(\\let\\label)o(st)o(yle)o(\\t)o(ext)o(sty)o(le)-79
282 y Fr(4)g Fx(\\lpad=1in)16 b(\\bpad=1cm)-79 332 y
Fr(5)62 b Fx(\\Graph{4in)o(,4)o(}{3)o(.5)o(in,)o(1in)o(})-79
382 y Fr(6)g Fx(\\To)18 b(\(0,0\))g(\(3.3,0\))76 b(\\hd{p})-79
432 y Fr(7)62 b Fx(\\To)18 b(\(0,0\))g(\(0,3.5\))76 b(\\hd{q})-79
482 y Fr(8)62 b Fx(\\Line)18 b(\(2,0\))f(\(2,3.25\))g(\\Line)h(\(0,1\))
f(\(3.2,1\))g(\\Dot)h(\(2,1\))-79 531 y Fr(9)62 b Fx(\\Dot)18
b(\(0,0\))-95 581 y Fr(10)61 b Fx(\045)-95 631 y Fr(11)g
Fx(\\Dot)18 b(\(2,0\))g(\\Dot)g(\(2.25,0\))e(\\Dot)i(\(2.5,0\))f(\\Dot)
h(\(2.75,0\))f(\\Dot)h(\(3,0\))-95 681 y Fr(12)61 b Fx(\045)-95
731 y Fr(13)g Fx(\\Dot)18 b(\(0,1\))g(\\Dot)g(\(0,1.25\))e(\\Dot)i
(\(0,1.5\))f(\\Dot)h(\(0,1.75\))-95 780 y Fr(14)61 b
Fx(\\Dot)18 b(\(0,2\))g(\\Dot)g(\(0,2.25\))e(\\Dot)i(\(0,2.5\))f(\\Dot)
h(\(0,2.75\))f(\\Dot)h(\(0,3\))-95 830 y Fr(15)61 b Fx(\045)-95
880 y Fr(16)g Fx(\\Line)18 b(\(0,2.25\))e(\(2.5,0\))37
b(^{d^p})17 b(:{.35,5pt})f(\\ro)-95 930 y Fr(17)61 b
Fx(\\Line)18 b(\(0,3\))f(\(3,0\))38 b(^{p)18 b(+)h(q)h(=)f(m)g(+)g(n})g
(:{.35,5pt})d(\\ro)-95 980 y Fr(18)61 b Fx(\045)-95 1029
y Fr(19)g Fx(\\Math{q)17 b(=)i(n})g(\(-.1,1\))e(*1)97
b(\\Math{E_{0)o(,p-)o(1})o(^2)16 b(=)j(E_{0,p-1}^p)o(})d(\(-.1,2.25\))g
(*1)-95 1079 y Fr(20)61 b Fx(\\Math{p)17 b(=)i(m})g(\(2,-.2\))e(*{.55})
g(\\Math{E_{p)o(,0})o(^2)f(=)j(E_{p,0}^p})d(\(2.75,-.2\))g(*{.6})-95
1129 y Fr(21)61 b Fx(\\endGraph)-95 1179 y Fr(22)g Fx($$)1020
2324 y
gsave
 1020 2324 a 1020 2324 a
currentpoint currentpoint translate 0 neg 15629758 atan rotate neg
exch neg exch translate
 1020 2324 a 525 2335 a
Fw(\000)-21 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)-21 b Fv(\021)1020 2324 y
grestore
 1020 2324 a 1505
2335 a FB(p)525 1799 y
gsave
 525 1799 a 525 1799 a
currentpoint currentpoint translate 16577001 neg 0 atan rotate neg
exch neg exch translate
 525 1799
a 0 1810 a Fw(\000)j(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)
g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)-18 b Fv(\021)525 1799
y
grestore
 525 1799 a 515 1285 a FB(q)1125 1837 y
gsave
 1125 1837 a
1125 1837 a
currentpoint currentpoint translate 15392929 neg 0 atan rotate neg
exch neg exch translate
 1125 1837 a 637 1847 a Fw(\000)c(\000)-9
b(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h
(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)
-21 b(\000)1125 1837 y
grestore
 1125 1837 a 1005 2024 a
gsave
 1005 2024
a 1005 2024 a
currentpoint currentpoint translate 0 neg 15156100 atan rotate neg
exch neg exch translate
 1005 2024 a 525 2035 a Fw(\000)j(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-17
b(\000)1005 2024 y
grestore
 1005 2024 a 1125 2024 a
gsave
 1125 2024
a 1125 2024 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 1125 2024 a 1115 2035 a Fw(\017)1125 2024
y
grestore
 1125 2024 a 525 2324 a
gsave
 525 2324 a 525 2324 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525 2324
a 515 2335 a Fw(\017)525 2324 y
grestore
 525 2324 a 1125 2324
a
gsave
 1125 2324 a 1125 2324 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 1125 2324 a 1115 2335 a Fw(\017)1125
2324 y
grestore
 1125 2324 a 1200 2324 a
gsave
 1200 2324 a 1200 2324
a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 1200 2324 a 1190 2335 a Fw(\017)1200 2324 y
grestore
 1200 2324
a 1275 2324 a
gsave
 1275 2324 a 1275 2324 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 1275 2324 a 1265
2335 a Fw(\017)1275 2324 y
grestore
 1275 2324 a 1350 2324 a
gsave
 1350
2324 a 1350 2324 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 1350 2324 a 1340 2335 a Fw(\017)1350
2324 y
grestore
 1350 2324 a 1425 2324 a
gsave
 1425 2324 a 1425 2324
a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 1425 2324 a 1415 2335 a Fw(\017)1425 2324 y
grestore
 1425 2324
a 525 2024 a
gsave
 525 2024 a 525 2024 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525 2024 a 515 2035
a Fw(\017)525 2024 y
grestore
 525 2024 a 525 1949 a
gsave
 525 1949 a
525 1949 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525 1949 a 515 1960 a Fw(\017)525 1949 y
grestore
 525
1949 a 525 1874 a
gsave
 525 1874 a 525 1874 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525 1874 a 515
1885 a Fw(\017)525 1874 y
grestore
 525 1874 a 525 1799 a
gsave
 525 1799
a 525 1799 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525 1799 a 515 1810 a Fw(\017)525 1799 y
grestore

525 1799 a 525 1724 a
gsave
 525 1724 a 525 1724 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525 1724
a 515 1735 a Fw(\017)525 1724 y
grestore
 525 1724 a 525 1649 a
gsave

525 1649 a 525 1649 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525 1649 a 515 1660 a Fw(\017)525
1649 y
grestore
 525 1649 a 525 1574 a
gsave
 525 1574 a 525 1574 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525
1574 a 515 1585 a Fw(\017)525 1574 y
grestore
 525 1574 a 525 1499
a
gsave
 525 1499 a 525 1499 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525 1499 a 515 1510 a Fw(\017)525
1499 y
grestore
 525 1499 a 525 1424 a
gsave
 525 1424 a 525 1424 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 525
1424 a 515 1435 a Fw(\017)525 1424 y
grestore
 525 1424 a 900 1987
a
gsave
 900 1987 a 900 1987 a
currentpoint currentpoint translate -10656643 neg 11840715 atan rotate
neg exch neg exch translate
 900 1987 a 396 1997 a Fw(\000)g(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)-16 b(\000)900 1987 y
grestore
 900 1987 a 900 1987 a
gsave
 900
1987 a 900 1987 a
currentpoint currentpoint translate -10656643 neg 11840715 atan rotate
neg exch neg exch translate
 900 1987 a 728 1954 a FB(d)750 1939
y Fu(p)749 1987 y
grestore
 749 1987 a 975 1874 a
gsave
 975 1874 a 975
1874 a
currentpoint currentpoint translate -14208858 neg 14208858 atan rotate
neg exch neg exch translate
 975 1874 a 339 1885 a Fw(\000)k(\000)j(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)e(\000)
975 1874 y
grestore
 975 1874 a 975 1874 a
gsave
 975 1874 a 975 1874
a
currentpoint currentpoint translate -14208858 neg 14208858 atan rotate
neg exch neg exch translate
 975 1874 a 655 1833 a FB(p)9 b FF(+)g FB(q)k FF(=)f
FB(m)d FF(+)h FB(n)784 1874 y
grestore
 784 1874 a 495 2024 a
gsave
 495
2024 a 495 2024 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 495 2024 a 395 2035 a FB(q)i FF(=)g
FB(n)495 2024 y
grestore
 495 2024 a 495 1649 a
gsave
 495 1649 a 495
1649 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 495 1649 a 202 1660 a FB(E)235 1645 y Fr(2)233
1670 y(0)p Fu(;p)p Fs(\000)p Fr(1)332 1660 y FF(=)g FB(E)409
1640 y Fu(p)407 1671 y Fr(0)p Fu(;p)p Fs(\000)p Fr(1)495
1649 y
grestore
 495 1649 a 1125 2384 a
gsave
 1125 2384 a 1125 2384 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate

1125 2384 a 1063 2395 a FB(p)f FF(=)h FB(m)1125 2384
y
grestore
 1125 2384 a 1350 2384 a
gsave
 1350 2384 a 1350 2384 a
currentpoint currentpoint translate 0 neg rotate neg exch neg exch
translate
 1350
2384 a 1225 2395 a FB(E)1258 2380 y Fr(2)1256 2405 y
Fu(p;)p Fr(0)1313 2395 y FF(=)g FB(E)1390 2375 y Fu(p)1388
2406 y(p;)p Fr(0)1350 2384 y
grestore
 1350 2384 a 954 2770 a FF(66)p
eop
%%Page: 67 11
67 66 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)-79 42 y Fr(1)62 b Fx($$)-79
91 y Fr(2)g Fx(\\rotatedla)o(be)o(ls)16 b(\\let\\label)o(sty)o(le)o
(\\te)o(xt)o(sty)o(le)g(\\scale=2)-79 141 y Fr(3)62 b
Fx(\\Diagram)-79 191 y Fr(4)82 b Fx(&)19 b(&)g(F\(3,2\))e(\\aLine)h
(\(1,-4\))f(>{F\(3,1,1)o(\)})f(:{.4})i(\\br)38 b(\\\\)-79
241 y Fr(5)82 b Fx(&)19 b(&)156 b(&)20 b(\\rdLine)d(>{F\(1,2,)o(2\)})f
(\\pt{right)o(,.7)o(5})g(\\\\)-79 291 y Fr(6)82 b Fx(&)19
b(&)156 b(&)177 b(&)19 b(F\(1,4\))370 b(\\\\)-79 340
y Fr(7)62 b Fx(F\(2,3\))17 b(\\aDash)h(\(4,1\))f(^{F\(1,1,3\))o(})g
(:{.4})g(\\pp)156 b(\\\\)-79 390 y Fr(8)82 b Fx(&)19
b(&)156 b(&)20 b(F\(4,1\))d(\\aLine)g(\(1,2\))h(>{F\(1,3,1)o(\)})75
b(\\\\)-79 440 y Fr(9)62 b Fx(\\Modify)-95 490 y Fr(10)f
Fx(\\Pt{top})17 b(\(2,4\))g(\\Pt{b1})g(\(0,1\))h(\\Pt{b2})f(\(3,0\))-95
540 y Fr(11)61 b Fx(\\Pt{LeftF})16 b(\(1.65,2\))g(\\Pt{BackF})g
(\(2,2.5\))-95 589 y Fr(12)61 b Fx(\\Pt{Bottom)o(F})16
b(\(2.5,1\))h(\\Pt{Right)o(F})f(\(3.1,2.25\))-95 639
y Fr(13)61 b Fx(\\Nul)38 b(\\pt{b1})17 b(\\pt{b2})271
b(\\pt{bottom,)o(.8)o(})-95 689 y Fr(14)61 b Fx(\\Nul)38
b(\\pt{Botto)o(mF)o(})17 b(\\pt{botto)o(m})94 b(\\pt{BottomL)o(,2)o(})
-95 739 y Fr(15)61 b Fx(\\Dash)18 b(\\pt{Botto)o(mF)o(})f(\\pt{botto)o
(m})94 b(\\tl\\circ)17 b(\\dt{3pt})-95 789 y Fr(16)61
b Fx(\\Line)18 b(\\pt{botto)o(m})e(\\pt{Bottom)o(L})94
b(\\hd{F\(1,1,2)o(,1)o(\)})-95 839 y Fr(17)61 b Fx(\\Line)18
b(\\pt{b1})f(\\pt{b2})g(_{F\(2,2,)o(1\)})35 b(\\br)-95
888 y Fr(18)61 b Fx(\\Nul)38 b(\\pt{b1})17 b(\\pt{top})251
b(\\pt{left,.2)o(5})16 b(\\pt{back,.)o(75)o(})-95 938
y Fr(19)61 b Fx(\\Nul)38 b(\\pt{BackF)o(})16 b(\\pt{back})173
b(\\pt{BackL,2)o(})-95 988 y Fr(20)61 b Fx(\\Nul)38 b(\\pt{LeftF)o(})16
b(\\pt{left})173 b(\\pt{LeftL,2)o(})-95 1038 y Fr(21)61
b Fx(\\Dash)18 b(\\pt{BackF)o(})e(\\pt{back})173 b(\\tl\\circ)17
b(\\dt{3pt})-95 1088 y Fr(22)61 b Fx(\\Line)18 b(\\pt{back})e
(\\pt{BackL)o(})173 b(\\hd{F\(1,1,1)o(,2)o(\)})-95 1137
y Fr(23)61 b Fx(\\Line)18 b(\\pt{b1})f(\\pt{top})f(<{F\(2,1,2\))o(})g
(\\br)-95 1187 y Fr(24)61 b Fx(\\Line)18 b(\\pt{LeftF)o(})e
(\\pt{LeftL})153 b(\\tl\\bullet)16 b(\\hd{F\(2,1,)o(1,1)o(\)})g(\\jt)j
(\\br)-95 1237 y Fr(25)61 b Fx(\\Nul)38 b(\\pt{Right)o(F})16
b(\\pt{right})133 b(\\pt{RightL,)o(3})-95 1287 y Fr(26)61
b Fx(\\Line)18 b(\\pt{Right)o(F})e(\\pt{RightL)o(})114
b(\\tl\\bullet)16 b(\\hd{F\(1,2,)o(1,1)o(\)})g(\\jt)j(\\br)-95
1337 y Fr(27)61 b Fx(\\endDiagra)o(m)-95 1386 y Fr(28)g
Fx($$)1029 2114 y
gsave
 1029 2114 a 1029 2114 a
currentpoint currentpoint translate 3729358 neg 14917432 atan rotate
neg exch neg exch translate
 1029 2114 a
608 2124 a Fv(\013)-8 b(\013)f(\013)g(\013)g(\013)g(\013)g(\013)g(\013)
g(\013)g(\013)g(\013)g(\013)g(\013)g(\013)g(\013)g(\013)g(\013)h(\013)f
(\013)g(\013)g(\013)g(\013)g(\013)g(\013)g(\013)g(\013)g(\013)g(\013)g
(\013)g(\013)g(\013)g(\013)g(\013)h(\013)f(\013)g(\013)1029
2114 y
grestore
 1029 2114 a 1029 2114 a
gsave
 1029 2114 a 1029 2114
a
currentpoint currentpoint translate 3729358 neg 14917432 atan rotate
neg exch neg exch translate
 1029 2114 a 863 2091 a FB(F)6 b FF(\(1)p FB(;)h FF(1)p
FB(;)g FF(3\))945 2114 y
grestore
 945 2114 a 1147 1996 a
gsave
 1147
1996 a 1147 1996 a
currentpoint currentpoint translate -14917432 neg 3729358 atan rotate
neg exch neg exch translate
 1147 1996 a 660 1996 a
1 setgray
 660 1996 a
690 2006 915 21 v 1147 1996 a
grestore
 1147 1996 a 1147 1996 a
gsave

1147 1996 a 1147 1996 a
currentpoint currentpoint translate -14917432 neg 3729358 atan rotate
neg exch neg exch translate
 1147 1996 a 690 2006 a Fw(\000)-18
b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)-17
b(\000)1147 1996 y
grestore
 1147 1996 a 1147 1996 a
gsave
 1147 1996
a 1147 1996 a
currentpoint currentpoint translate -14917432 neg 3729358 atan rotate
neg exch neg exch translate
 1147 1996 a 973 1973 a FB(F)6 b FF(\(3)p
FB(;)h FF(1)p FB(;)g FF(1\))1055 1996 y
grestore
 1055 1996 a 1265
1760 a
gsave
 1265 1760 a 1265 1760 a
currentpoint currentpoint translate -7458716 neg 7458716 atan rotate
neg exch neg exch translate
 1265 1760 a 968 1770 a
Fw(\000)-17 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)
f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)h(\000)-17 b(\000)1265
1760 y
grestore
 1265 1760 a 1265 1760 a
gsave
 1265 1760 a 1265 1760
a
currentpoint currentpoint translate -7458716 neg 7458716 atan rotate
neg exch neg exch translate
 1265 1760 a 1183 1737 a FB(F)6 b FF(\(1)p FB(;)h FF(2)p
FB(;)g FF(2\))1265 1760 y
grestore
 1265 1760 a 1383 2232 a
gsave
 1383
2232 a 1383 2232 a
currentpoint currentpoint translate 7458716 neg 3729358 atan rotate
neg exch neg exch translate
 1383 2232 a 1150 2242 a Fw(\000)-12
b(\000)j(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)e(\000)1383
2232 y
grestore
 1383 2232 a 1383 2232 a
gsave
 1383 2232 a 1383 2232
a
currentpoint currentpoint translate 7458716 neg 3729358 atan rotate
neg exch neg exch translate
 1383 2232 a 1301 2276 a FB(F)6 b FF(\(1)p FB(;)h FF(3)p
FB(;)g FF(1\))1383 2232 y
grestore
 1383 2232 a 966 1534 a FB(F)f
FF(\(3)p FB(;)h FF(2\))1439 2006 y FB(F)f FF(\(1)p FB(;)h
FF(4\))494 2242 y FB(F)f FF(\(2)p FB(;)h FF(3\))1202
2479 y FB(F)f FF(\(4)p FB(;)h FF(1\))910 2350 y
gsave
 910 2350
a 910 2350 a
currentpoint currentpoint translate -3729358 neg 11188074 atan rotate
neg exch neg exch translate
 910 2350 a 910 2350 a
grestore
 910 2350 a 1113 2320
a
gsave
 1113 2320 a 1113 2320 a
currentpoint currentpoint translate -2770849 neg -1058864 atan rotate
neg exch neg exch translate
 1113 2320 a 1113 2320 a
grestore
 1113
2320 a 1113 2320 a
gsave
 1113 2320 a 1113 2320 a
currentpoint currentpoint translate -2770849 neg -1058864 atan rotate
neg exch neg exch translate
 1113 2320
a 1025 2330 a Fv(\013)-9 b(\013)g(\013)g(\013)g(\013)g(\013)g(\013)1113
2320 y
grestore
 1113 2320 a 1136 2242 a Fw(\016)1050 2484 y
gsave
 1050
2484 a 1050 2484 a
currentpoint currentpoint translate -2405159 neg -921240 atan rotate
neg exch neg exch translate
 1050 2484 a 981 2494 a Fw(\000)-23
b(\000)-9 b(\000)g(\000)h(\000)-22 b(\000)1050 2484 y
grestore

1050 2484 a 920 2570 a FB(F)6 b FF(\(1)p FB(;)h FF(1)p
FB(;)g FF(2)p FB(;)g FF(1\))910 2350 y
gsave
 910 2350 a 910
2350 a
currentpoint currentpoint translate -3729358 neg 11188074 atan rotate
neg exch neg exch translate
 910 2350 a 537 2350 a
1 setgray
 537 2350 a 614 2361 597
21 v 910 2350 a
grestore
 910 2350 a 910 2350 a
gsave
 910 2350 a 910
2350 a
currentpoint currentpoint translate -3729358 neg 11188074 atan rotate
neg exch neg exch translate
 910 2350 a 614 2361 a Fw(\000)-16 b(\000)-9 b(\000)h(\000)f
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g
(\000)-15 b(\000)910 2350 y
grestore
 910 2350 a 910 2350 a
gsave
 910
2350 a 910 2350 a
currentpoint currentpoint translate -3729358 neg 11188074 atan rotate
neg exch neg exch translate
 910 2350 a 830 2394 a FB(F)6 b FF(\(2)p
FB(;)h FF(2)p FB(;)g FF(1\))912 2350 y
grestore
 912 2350 a 792
1878 a
gsave
 792 1878 a 792 1878 a
currentpoint currentpoint translate 11188074 neg 7458716 atan rotate
neg exch neg exch translate
 792 1878 a 792 1878 a
grestore
 792
1878 a 965 1796 a
gsave
 965 1796 a 965 1796 a
currentpoint currentpoint translate 2578128 neg -2008000 atan rotate
neg exch neg exch translate
 965 1796 a 965
1796 a
grestore
 965 1796 a 815 2018 a
gsave
 815 2018 a 815 2018 a
currentpoint currentpoint translate -713450 neg -4145418 atan rotate
neg exch neg exch translate
 815
2018 a 815 2018 a
grestore
 815 2018 a 965 1796 a
gsave
 965 1796 a 965
1796 a
currentpoint currentpoint translate 2578128 neg -2008000 atan rotate
neg exch neg exch translate
 965 1796 a 865 1807 a Fv(\013)-9 b(\013)g(\013)g(\013)g(\013)g
(\013)g(\013)g(\013)965 1796 y
grestore
 965 1796 a 1018 1888 a
Fw(\016)845 1643 y
gsave
 845 1643 a 845 1643 a
currentpoint currentpoint translate 2271420 neg -1768140 atan rotate
neg exch neg exch translate
 845 1643 a 767
1653 a Fw(\000)-16 b(\000)-9 b(\000)g(\000)g(\000)-14
b(\000)845 1643 y
grestore
 845 1643 a 688 1581 a FB(F)6 b FF(\(1)p
FB(;)h FF(1)p FB(;)g FF(1)p FB(;)g FF(2\))792 1878 y
gsave

792 1878 a 792 1878 a
currentpoint currentpoint translate 11188074 neg 7458716 atan rotate
neg exch neg exch translate
 792 1878 a 367 1878 a
1 setgray
 367 1878
a 400 1888 786 21 v 792 1878 a
grestore
 792 1878 a 792 1878 a
gsave

792 1878 a 792 1878 a
currentpoint currentpoint translate 11188074 neg 7458716 atan rotate
neg exch neg exch translate
 792 1878 a 400 1888 a Fw(\000)-14
b(\000)-9 b(\000)h(\000)f(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)d(\000)792 1878 y
grestore
 792 1878 a 792
1878 a
gsave
 792 1878 a 792 1878 a
currentpoint currentpoint translate 11188074 neg 7458716 atan rotate
neg exch neg exch translate
 792 1878 a 710 1855 a FB(F)6
b FF(\(2)p FB(;)h FF(1)p FB(;)g FF(2\))792 1878 y
grestore
 792
1878 a 696 2039 a
gsave
 696 2039 a 696 2039 a
currentpoint currentpoint translate -1363986 neg -7905486 atan rotate
neg exch neg exch translate
 696 2039 a 441
2039 a
1 setgray
 441 2039 a 437 2049 402 21 v 696 2039 a
grestore
 696 2039
a 696 2039 a
gsave
 696 2039 a 696 2039 a
currentpoint currentpoint translate -1363986 neg -7905486 atan rotate
neg exch neg exch translate
 696 2039 a 437 2049
a Fw(\000)-20 b(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-20
b(\000)696 2039 y
grestore
 696 2039 a 936 2006 a Fw(\017)344 2093
y FB(F)6 b FF(\(2)p FB(;)h FF(1)p FB(;)g FF(1)p FB(;)g
FF(1\))1329 1901 y
gsave
 1329 1901 a 1329 1901 a
currentpoint currentpoint translate 1139925 neg 1284136 atan rotate
neg exch neg exch translate
 1329 1901
a 1329 1901 a
grestore
 1329 1901 a 1397 1841 a
gsave
 1397 1841 a 1397
1841 a
currentpoint currentpoint translate 3030492 neg 3415941 atan rotate
neg exch neg exch translate
 1397 1841 a 1252 1841 a
1 setgray
 1252 1841 a 1248 1851
254 21 v 1397 1841 a
grestore
 1397 1841 a 1397 1841 a
gsave
 1397 1841
a 1397 1841 a
currentpoint currentpoint translate 3030492 neg 3415941 atan rotate
neg exch neg exch translate
 1397 1841 a 1248 1851 a Fw(\000)-14 b(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)-13
b(\000)1397 1841 y
grestore
 1397 1841 a 1278 1947 a Fw(\017)1403
1755 y FB(F)6 b FF(\(1)p FB(;)h FF(2)p FB(;)g FF(1)p
FB(;)g FF(1\))954 2770 y(67)p eop
%%Page: 68 12
68 67 bop 0 -58 a Fz(T)o(yp)q(esetting)9 b(diagrams)g(with)j(kuvio.tex)
1145 b(Revision)10 b(2.5.12)-79 42 y Fr(1)62 b Fx($$)-79
91 y Fr(2)g Fx(\\def\\y#1#2)o({Y)o(\(#1)o(,#)o(2\)})16
b(\\def\\RP{{)o(\\bb)g(R}P})-79 141 y Fr(3)62 b Fx(\\gravitate)o(ri)o
(ght)-79 191 y Fr(4)g Fx(\\Dg)-79 241 y Fr(5)g Fx(&&&\\RP^1)17
b(=)i({}&)f(\\y11)g(&)i(\\rInto)d(&)i(\\y21)f(&)h(\\rInto)f(&)h(\\y31)f
(&)h(\\rInto)e(&)j(\\y41)e(&)h(\\rInto)e(&)i(\\cdots)f(\\\\)-79
291 y Fr(6)62 b Fx(&&&)195 b(&)117 b(&)157 b(&)19 b(\\dTo)f(&)157
b(&)19 b(\\dTo)f(&)156 b(&)20 b(\\dTo)e(&)333 b(\\\\)-79
340 y Fr(7)62 b Fx(&&\\RP^2)17 b(=)i({}&&)116 b(&)157
b(&)19 b(\\y12)f(&)h(\\rInto)f(&)h(\\y22)f(&)h(\\rInto)e(&)j(\\y32)e(&)
h(\\rInto)e(&)i(\\cdots)f(\\\\)-79 390 y Fr(8)62 b Fx(&&)195
b(&&)117 b(&)157 b(&)117 b(&)157 b(&)19 b(\\dTo)f(&)156
b(&)20 b(\\dTo)e(&)333 b(\\\\)-79 440 y Fr(9)62 b Fx(&\\RP^3)17
b(=)j({}&&&)115 b(&)157 b(&)117 b(&)157 b(&)19 b(\\y13)f(&)h(\\rInto)e
(&)j(\\y23)e(&)h(\\rInto)e(&)i(\\cdots)f(\\\\)-95 490
y Fr(10)61 b Fx(&)196 b(&&&)116 b(&)157 b(&)117 b(&)157
b(&)117 b(&)156 b(&)20 b(\\dTo)e(&)333 b(\\\\)-95 540
y Fr(11)61 b Fx(\\RP^4)18 b(=)h({}&&&&)115 b(&)157 b(&)117
b(&)157 b(&)117 b(&)156 b(&)20 b(\\y14)e(&)h(\\rInto)e(&)i(\\cdots)f
(\\\\)-95 589 y Fr(12)61 b Fx(\\endDg)-95 639 y Fr(13)g
Fx($$)666 781 y
gsave
 666 781 a 666 781 a
currentpoint currentpoint translate 0 neg 4406548 atan rotate neg exch
neg exch translate
 666 781 a 597 791
a FB(,)-7 b Fw(\000)-22 b(\000)-9 b(\000)g(\000)g(\000)-21
b Fv(\021)666 781 y
grestore
 666 781 a 945 781 a
gsave
 945 781 a 945
781 a
currentpoint currentpoint translate 0 neg 4406548 atan rotate neg exch
neg exch translate
 945 781 a 876 791 a FB(,)-7 b Fw(\000)-22 b(\000)-9
b(\000)g(\000)g(\000)-21 b Fv(\021)945 781 y
grestore
 945 781
a 1224 781 a
gsave
 1224 781 a 1224 781 a
currentpoint currentpoint translate 0 neg 4406548 atan rotate neg exch
neg exch translate
 1224 781 a 1155 791
a FB(,)-7 b Fw(\000)-22 b(\000)-9 b(\000)g(\000)g(\000)-21
b Fv(\021)1224 781 y
grestore
 1224 781 a 1484 781 a
gsave
 1484 781 a
1484 781 a
currentpoint currentpoint translate 0 neg 3797606 atan rotate neg exch
neg exch translate
 1484 781 a 1434 791 a FB(,)-7 b Fw(\000)-21
b(\000)-10 b(\000)i(\000)f(\000)-21 b Fv(\021)1484 781
y
grestore
 1484 781 a 805 875 a
gsave
 805 875 a 805 875 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 805 875 a
740 886 a Fw(\000)e(\000)-9 b(\000)g(\000)h(\000)-22
b Fv(\021)805 875 y
grestore
 805 875 a 1084 875 a
gsave
 1084 875 a 1084
875 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1084 875 a 1019 886 a Fw(\000)f(\000)-8 b(\000)f(\000)g(\000)-22
b Fv(\021)1084 875 y
grestore
 1084 875 a 1363 875 a
gsave
 1363 875 a
1363 875 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1363 875 a 1298 886 a Fw(\000)g(\000)-9 b(\000)g(\000)g
(\000)-22 b Fv(\021)1363 875 y
grestore
 1363 875 a 945 970 a
gsave
 945
970 a 945 970 a
currentpoint currentpoint translate 0 neg 4406548 atan rotate neg exch
neg exch translate
 945 970 a 876 980 a FB(,)-7 b Fw(\000)-22
b(\000)-9 b(\000)g(\000)g(\000)-21 b Fv(\021)945 970
y
grestore
 945 970 a 1224 970 a
gsave
 1224 970 a 1224 970 a
currentpoint currentpoint translate 0 neg 4406548 atan rotate neg exch
neg exch translate
 1224 970
a 1155 980 a FB(,)-7 b Fw(\000)-22 b(\000)-9 b(\000)g(\000)g(\000)-21
b Fv(\021)1224 970 y
grestore
 1224 970 a 1484 970 a
gsave
 1484 970 a
1484 970 a
currentpoint currentpoint translate 0 neg 3797606 atan rotate neg exch
neg exch translate
 1484 970 a 1434 980 a FB(,)-7 b Fw(\000)-21
b(\000)-10 b(\000)i(\000)f(\000)-21 b Fv(\021)1484 970
y
grestore
 1484 970 a 1084 1064 a
gsave
 1084 1064 a 1084 1064 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1084
1064 a 1019 1075 a Fw(\000)e(\000)-8 b(\000)f(\000)g(\000)-22
b Fv(\021)1084 1064 y
grestore
 1084 1064 a 1363 1064 a
gsave
 1363 1064
a 1363 1064 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1363 1064 a 1298 1075 a Fw(\000)g(\000)-9
b(\000)g(\000)g(\000)-22 b Fv(\021)1363 1064 y
grestore
 1363 1064
a 1224 1159 a
gsave
 1224 1159 a 1224 1159 a
currentpoint currentpoint translate 0 neg 4406548 atan rotate neg exch
neg exch translate
 1224 1159 a 1155
1169 a FB(,)-7 b Fw(\000)-22 b(\000)-9 b(\000)g(\000)g(\000)-21
b Fv(\021)1224 1159 y
grestore
 1224 1159 a 1484 1159 a
gsave
 1484 1159
a 1484 1159 a
currentpoint currentpoint translate 0 neg 3797606 atan rotate neg exch
neg exch translate
 1484 1159 a 1434 1169 a FB(,)-7 b Fw(\000)-21
b(\000)-10 b(\000)i(\000)f(\000)-21 b Fv(\021)1484 1159
y
grestore
 1484 1159 a 1363 1253 a
gsave
 1363 1253 a 1363 1253 a
currentpoint currentpoint translate -2983488 neg 0 atan rotate neg
exch neg exch translate
 1363
1253 a 1298 1264 a Fw(\000)f(\000)-9 b(\000)g(\000)g(\000)-22
b Fv(\021)1363 1253 y
grestore
 1363 1253 a 1484 1348 a
gsave
 1484 1348
a 1484 1348 a
currentpoint currentpoint translate 0 neg 3797606 atan rotate neg exch
neg exch translate
 1484 1348 a 1434 1358 a FB(,)-7 b Fw(\000)-21
b(\000)-10 b(\000)i(\000)f(\000)-21 b Fv(\021)1484 1348
y
grestore
 1484 1348 a 322 791 a Fo(R)p FB(P)390 774 y Fr(1)419
791 y FF(=)12 b FB(Y)d FF(\(1)p FB(;)e FF(1\))153 b FB(Y)10
b FF(\(2)p FB(;)d FF(1\))152 b FB(Y)10 b FF(\(3)p FB(;)d
FF(1\))153 b FB(Y)9 b FF(\(4)p FB(;)e FF(1\))153 b Fw(\001)7
b(\001)g(\001)601 980 y Fo(R)p FB(P)669 963 y Fr(2)698
980 y FF(=)12 b FB(Y)e FF(\(1)p FB(;)d FF(2\))152 b FB(Y)10
b FF(\(2)p FB(;)d FF(2\))153 b FB(Y)9 b FF(\(3)p FB(;)e
FF(2\))153 b Fw(\001)7 b(\001)g(\001)880 1169 y Fo(R)p
FB(P)948 1152 y Fr(3)978 1169 y FF(=)k FB(Y)f FF(\(1)p
FB(;)d FF(3\))153 b FB(Y)9 b FF(\(2)p FB(;)e FF(3\))153
b Fw(\001)7 b(\001)g(\001)1159 1358 y Fo(R)p FB(P)1227
1341 y Fr(4)1257 1358 y FF(=)12 b FB(Y)d FF(\(1)p FB(;)e
FF(4\))153 b Fw(\001)7 b(\001)g(\001)-79 1523 y Fr(1)62
b Fx($$)-79 1573 y Fr(2)g Fx(\\def\\M{{\\c)o(al)16 b(M}\\dot})h
(\\def\\inv{)o(^{-)o(1})o(})g(\\def\\orlz)o(#1)o({\\l)o(ang)o(le)o
(#1\\)o(ra)o(ngl)o(e})-79 1623 y Fr(3)62 b Fx(\\let\\label)o(st)o(yle)o
(\\t)o(ext)o(sty)o(le)-79 1673 y Fr(4)g Fx(\\Dg)-79 1722
y Fr(5)g Fx([q\(g,b\),t])16 b(\\aNul)h(\(1,-1\))h(\\aMapsto)e(\(2,-4\))
i(&&&)g(\\rMapsto)f(&&&)-79 1772 y Fr(6)395 b Fx(q\(g,\\phi\(b,)o(t\))o
(\))17 b(\\aNul)g(\(-1,-1\))g(\\aMapsto)g(\(-2,-4\))g(\\mx{12pt})f
(\\\\)-79 1822 y Fr(7)199 b Fx(&)20 b(\\M)e(R_s)h(&)137
b(&)19 b(\\rTo)77 b(&)156 b(&)20 b(\\beta\\inv)o(\(W)o(_s\))55
b(\\\\)-79 1872 y Fr(8)199 b Fx(&)157 b(&)19 b(\\rdTo)f(&)176
b(&)19 b(\\ldTo)f(>{R_s})272 b(\\\\)-79 1922 y Fr(9)199
b Fx(&)157 b(&)137 b(&)19 b(\\beta\\inv)o(\\or)o(lz{)o(s})369
b(\\\\)-95 1971 y Fr(10)198 b Fx(&)39 b(&)19 b(q\(g,r_s\(b\)\))d(&)j
({})g(=)g({})g(&)g(q\(g,r_s\(\\p)o(hi)o(\(b,)o(t\)\))o(\))350
b(\\\\)-95 2021 y Fr(11)61 b Fx(\\endDg)-95 2071 y Fr(12)g
Fx($$)676 2255 y
gsave
 676 2255 a 676 2255 a
currentpoint currentpoint translate -1491744 neg 2797019 atan rotate
neg exch neg exch translate
 676 2255 a 676
2255 a
grestore
 676 2255 a 706 2397 a
gsave
 706 2397 a 706 2397 a
currentpoint currentpoint translate -5966976 neg 3747163 atan rotate
neg exch neg exch translate
 706
2397 a 516 2407 a Fw(7\000)-13 b(\000)k(\000)g(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)d
Fv(\021)706 2397 y
grestore
 706 2397 a 967 2208 a
gsave
 967 2208 a 967
2208 a
currentpoint currentpoint translate 0 neg 11974508 atan rotate neg
exch neg exch translate
 967 2208 a 679 2218 a Fw(7\000)c(\000)-9 b(\000)g(\000)g(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)h(\000)f
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-15
b Fv(\021)967 2208 y
grestore
 967 2208 a 1232 2255 a
gsave
 1232 2255
a 1232 2255 a
currentpoint currentpoint translate -1491744 neg -3583451 atan rotate
neg exch neg exch translate
 1232 2255 a 1232 2255 a
grestore
 1232 2255 a 1225
2397 a
gsave
 1225 2397 a 1225 2397 a
currentpoint currentpoint translate -5966976 neg -3819525 atan rotate
neg exch neg exch translate
 1225 2397 a 1033 2407
a Fw(7\000)-23 b(\000)-9 b(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g
(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-22
b Fv(\021)1225 2397 y
grestore
 1225 2397 a 942 2303 a
gsave
 942 2303
a 942 2303 a
currentpoint currentpoint translate 0 neg 5594038 atan rotate neg exch
neg exch translate
 942 2303 a 822 2313 a Fw(\000)k(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)h(\000)-18 b Fv(\021)942
2303 y
grestore
 942 2303 a 853 2397 a
gsave
 853 2397 a 853 2397 a
currentpoint currentpoint translate -2983488 neg 2797019 atan rotate
neg exch neg exch translate
 853
2397 a 755 2407 a Fw(\000)f(\000)-9 b(\000)g(\000)g(\000)g(\000)g(\000)
-17 b Fv(\021)853 2397 y
grestore
 853 2397 a 1030 2397 a
gsave
 1030
2397 a 1030 2397 a
currentpoint currentpoint translate -2983488 neg -2797019 atan rotate
neg exch neg exch translate
 1030 2397 a 937 2407 a Fw(\000)c(\000)-9
b(\000)g(\000)g(\000)g(\000)g(\000)-20 b Fv(\021)1030
2397 y
grestore
 1030 2397 a 1030 2397 a
gsave
 1030 2397 a 1030 2397
a
currentpoint currentpoint translate -2983488 neg -2797019 atan rotate
neg exch neg exch translate
 1030 2397 a 1027 2385 a
currentpoint currentpoint translate 2983488 neg -2797019 atan rotate
neg exch neg exch translate
 1027 2385 a 28 x FB(R)1059
2419 y Fu(s)1027 2397 y
grestore
 1027 2397 a 504 2218 a FF([)p
FB(q)q FF(\()p FB(g)q(;)7 b(b)p FF(\))p FB(;)g(t)p FF(])574
b FB(q)q FF(\()p FB(g)q(;)7 b(\036)p FF(\()p FB(b;)g(t)p
FF(\)\))715 2313 y Fw(M)778 2302 y FF(_)765 2313 y FB(R)797
2319 y Fu(s)1039 2313 y FB(\014)1064 2296 y Fs(\000)p
Fr(1)1109 2313 y FF(\()p FB(W)1164 2319 y Fu(s)1182 2313
y FF(\))881 2502 y FB(\014)906 2485 y Fs(\000)p Fr(1)951
2502 y Fw(h)p FB(s)p Fw(i)735 2596 y FB(q)q FF(\()p FB(g)q(;)g(r)830
2602 y Fu(s)848 2596 y FF(\()p FB(b)p FF(\)\))k(=)h FB(q)q
FF(\()p FB(g)q(;)7 b(r)1064 2602 y Fu(s)1082 2596 y FF(\()p
FB(\036)p FF(\()p FB(b;)g(t)p FF(\)\)\))954 2770 y(68)p
eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF