diff options
author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
---|---|---|
committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/generic/diagrams/kuvio/examples.ps |
Initial commit
Diffstat (limited to 'macros/generic/diagrams/kuvio/examples.ps')
-rw-r--r-- | macros/generic/diagrams/kuvio/examples.ps | 5423 |
1 files changed, 5423 insertions, 0 deletions
diff --git a/macros/generic/diagrams/kuvio/examples.ps b/macros/generic/diagrams/kuvio/examples.ps new file mode 100644 index 0000000000..7b547ab9eb --- /dev/null +++ b/macros/generic/diagrams/kuvio/examples.ps @@ -0,0 +1,5423 @@ +%!PS-Adobe-2.0 +%%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software +%%Title: tdwk.dvi +%%Pages: 12 0 +%%PageOrder: Ascend +%%BoundingBox: 0 0 612 792 +%%EndComments +%DVIPSCommandLine: dvips -D300 tdwk -o +%DVIPSParameters: dpi=300, comments removed +%DVIPSSource: TeX output 1996.06.09:1515 +%%BeginProcSet: tex.pro +/TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N +/X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 +mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} +ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale +isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div +hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul 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+(\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 + 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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 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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 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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 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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 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+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 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-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 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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 + 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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 |