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diff --git a/Master/texmf-dist/doc/latex/spectralsequences/examples/example_ass.tex b/Master/texmf-dist/doc/latex/spectralsequences/examples/example_ass.tex new file mode 100644 index 00000000000..fcfca3ae84c --- /dev/null +++ b/Master/texmf-dist/doc/latex/spectralsequences/examples/example_ass.tex @@ -0,0 +1,359 @@ +%% +%% Package: spectralsequences.sty version 1.0 +%% Author: Hood Chatham +%% Email: hood@mit.edu +%% Date: 2017-06-18 +%% License: Latex Project Public License +%% +%% File: example_ass.tex +%% +%% Draws the Adams Spectral Sequence at the prime 2 through the 45 stem. +%% See pages 146 - 147 of Green book +%% https://mathoverflow.net/questions/102316/differentials-in-the-adams-spectral-sequence-for-spheres-at-the-prime-p-2 +%% https://en.wikipedia.org/wiki/Homotopy_groups_of_spheres#Table_of_stable_homotopy_groups +%% + + +\documentclass{article} +\usepackage[landscape,paperheight=14in,margin=0.1in]{geometry} +\usepackage{spectralsequences} + + +\begin{document} +\NewSseqGroup\tower {m} { + \class(0,0) + \foreach \y in {2,...,#1} { + \class(0, \y-1) + \structline(0, \y-2, -1)(0, \y-1, -1) + } +} + +\def\etaclass(#1,#2){ + \class(#1+1,#2+1) + \structline(#1,#2, -1)(#1+1,#2+1, -1) +} +\def\etasqclass(#1,#2){ + \class(#1+1,#2+1) + \class(#1+2,#2+2) + \structline(#1,#2, -1)(#1+1,#2+1, -1) + \structline(#1+1,#2+1, -1)(#1+2,#2+2, -1) +} +\def\etacubclass(#1,#2){ + \class(#1+1,#2+1) + \class(#1+2,#2+2) + \class(#1+3,#2+3) + \structline(#1,#2, -1)(#1+1,#2+1, -1) + \structline(#1+1,#2+1, -1)(#1+2,#2+2, -1) + \structline(#1+2,#2+2, -1)(#1+3,#2+3, -1) +} +\def\divtwoclass[#1](#2,#3){ + \class[#1](#2,#3-1) + \structline(#2,#3-1,-1)(#2,#3 ,-1) +} +\def\divfourclass[#1](#2,#3){ + \class(#2,#3-1) + \structline(#2,#3-1,-1)(#2,#3 ,-1) + \class[#1](#2,#3-2) + \structline(#2,#3-2,-1)(#2,#3-1,-1) +} +\def\diveightclass[#1](#2,#3){ + \class(#2,#3-1) + \structline(#2,#3-1,-1)(#2,#3 ,-1) + \class(#2,#3-2) + \structline(#2,#3-2,-1)(#2,#3-1,-1) + \class[#1](#2,#3-3) + \structline(#2,#3-3,-1)(#2,#3-2,-1) + +} +\def\nuclass(#1,#2){ + \class(#1+3,#2+1) + \structline(#1,#2,-1)(#1+3,#2+1,-1) +} +\def\nustruct(#1,#2){ + \structline(#1,#2,-1)(#1+3,#2+1,-1) +} + +\begin{sseqdata}[ + name = S0ASS, + Adams grading, + classes=fill, + class labels={above left=0.2em}, + x range={0}{45}, + y range={0}{23}, + xscale=0.7, + yscale=0.8, + differentials = red, + right clip padding = 3em, + classes = { tooltip = { (\xcoord,\ycoord) } }, + grid = go +] +\tower(0,0){25} + +% multiples of eta +\etacubclass(0,0) +\classoptions["h_1"](1,1) + +% divisibilities of nu +\divfourclass["h_2" below](3,3) + +\nustruct(0,0) + +\nuclass(3,1) + + + +\tower(7,1){4} +%\classoptions["h_3" left](7,1) +\etasqclass(7,1) +\structline(6,2)(9,3) + +\class["c_0" above](8,3) +\etaclass(8,3) + + + +\class["Ph_1"](9,5) +\etasqclass(9,5) +\divfourclass["Ph_2" below](11,7) + +\tower(14,2){2} +\classoptions["h_3^2" left](14,2) +\tower(14,4){3} +\classoptions["d_0" left](14,4) + +\tower(15,1){8} +\classoptions["h_4" left](15,1) +\d2(15,1) % d2(h_4) = h_0h_3^2 +\d3(15,2)\d3(15,3) % d2(h_0h_4) = h_0d_0 + +\etacubclass(15,1) +\divfourclass[](18,4) +\nustruct(15,1)\nustruct(15,2)\nustruct(15,3) + + +\nuclass(18,2) + +\etacubclass(14,4) +\diveightclass["e_0" left](17,7) +\nustruct(14,6)\nustruct(14,5)\nustruct(14,4) + +\nuclass(17,5) +\divfourclass["g" {below = 0.3em}](20,6) +\etaclass(17,4) +\divtwoclass["f_0" {below right=0em}](18,5) +\etaclass(20,4) +\nustruct(18,4) + +\classoptions["h_3^3" below](21,3) + +\d2(17,4)\d2(18,5)\d2(18,4,-1) % d2(e_0) = h1^2 d0, d2(f_0) = h0^2 e0 +\nustruct(17,4)\nuclass(20,5) +\divtwoclass[](23,6)\nustruct(20,4) +\nuclass(23,5) + +\tower(23,7){6} +\classoptions["i" left](23,7) + +\class["Pc_0" {xshift=3pt}](16,7)\etaclass(16,7) +\class["P^2c_0" {xshift=5pt,yshift=2pt}](24,11)\etaclass(24,11) + +\class["c_1" {above=0em}](19,3) +\nuclass(19,3) + +\class["h_4c_0" below](23,4) +\etaclass(23,4) + + +\class["P^2h_1"](17,9)\etasqclass(17,9) +\divfourclass["P^2h_2" {below=0em}](19,11) +\nuclass(19,9) +\divfourclass["Pd_0" left](22,10) +\etacubclass(22,8) +\diveightclass["Pe_0" below](25,11) +\etaclass(25,8)\divfourclass["j" below](26,9) +\d2(23,7)\d2(23,8) % d2(i)=h_0Pd_0 +\d2(25,8) % d2(Pe_0) = h_1^2 Pd +\d2(26,9)\d2(26,8)\d2(26,7) % d2(j) = h_0 Pe_0 + +\nustruct(22,10)\nustruct(22,9)\nustruct(22,8) + + +\class["P^3h_1"](25,13)\etasqclass(25,13) +\divfourclass["P^3h_2" {below=0em}](27,15) +\nuclass(27,13) +\divfourclass["P^2d_0" {left=0.2em}](30,14) +\etacubclass(30,12) +\diveightclass["P^2e_0" {below=0em}](33,15) +\d2(33,12) % d2(P^2e_0) = h_1^2 P^2d_0 +\nustruct(30,14)\nustruct(30,13)\nustruct(30,12) +\etaclass(33,12) +\divfourclass["Pj" {right}](34,13) +\d2(34,11)\d2(34,12)\d2(34,13) % d2(Pj) = h0 P^2e_0 + + + +\class(28,10)\divfourclass["{Pg=d_0^2}" {below left=-0.5em}](28,10) +\etaclass(28,8)\divfourclass["k" below](29,9) +\d2(29,7)\d2(29,8) % d2(k) = h_0 Pg = h_0 d_0^2 +\class["r" below](30,6) \d3(30,6) % d3(r) = h0^2 k +\tower(30,7){5} +\classoptions["s" below](30,7) + +\tower(30,2){4} +\classoptions["h_4^2" below](30,2) +\etaclass(30,2) + +\tower(31,1){16}\classoptions["h_5" below](31,1) +\d2(31,1)\d2(31,2)\d2(31,3,-1) % d2(h_5) = h_0 h_4^2 +\d3(31,4)\d3(31,5)\d3(31,6)\d3(31,7) \d3(31,8,1) % \d3(h_0^3 h_5) = s +\replaceclass[offset={(0,0)}](31,8) % d_0e_0 + h_0^7h_5 +\structline(31,8)(31,9) +\d4(31,8)\d4(31,9)\d4(31,10) % d4(d_0e_0 + h_0^7h_5) = P^2d_0, d4(h_0^8 h_5) = h_0 P^2d_0 +\etacubclass(31,1) +\divfourclass[](34,4) +\nustruct(31,3)\nustruct(31,2)\nustruct(31,1) +\nuclass(34,2) + +\class["n" above](31,5)\nuclass(31,5) + +\class(31,10) +\divfourclass["d_0e_0" {below right=0em,xshift=-5pt}](31,10) +\etaclass(31,8) +\divfourclass["l" {right=0em}](32,9) +\d3(31,8,-1) % d3(d_0e_0) = h_0^4 s = d3(h_0^7 h_5), see replaceclass above + +\d2(32,7,,-1)\d2(32,8,,-1) % d2(l) = h_0 d_0 e_0 +\d4(32,9,-1) % d4(h_0^2 l) = h_1 P^2d_0 + +\class["q"](32,6)\etaclass(32,6) + +\class["d_1"](32,4)\etaclass(32,4) +\nuclass(32,4)\nuclass(35,5) +\divtwoclass["p" above right](33,5) + +\class["P^3c_0"{xshift=4pt,yshift=2pt}](32,15)\etaclass(32,15) + +\class["P^4h_1"](33,17)\etasqclass(33,17) +\divfourclass["P^4h_2" right](35,19) + +\class(34,10) +\divfourclass["d_0g" left](34,10) +\etaclass(34,8) +\divfourclass["m" right](35,9) +\d2(35,7)\d2(35,8) % d2(m) = h_0 d_0 g + + +\class["t"](36,6)\etaclass(36,6) +\nustruct(34,6) + +\class(36,14) +\divfourclass["P^2g" left](36,14) +\etaclass(36,12) +\divfourclass["Pk" {right=0em}](37,13) +\d2(37,11)\d2(37,12) % d_2(P^1k) = h_0 P^2g + + +\tower(37,5){6}\classoptions["x"](37,5) + +\class["e_0g"](37,8)\etaclass(37,8) +\diveightclass["y" right](38,9) +\d4(37,8,-1) \d4(38,9)% d4(e_0g) = P^2g +\d2(38,6,-1)\d2(38,7,-1)\d2(38,8,-1) % d2(y) = h_0^3x + +\class(38,5) +\diveightclass["h_3h_5" below](38,5) +\etasqclass(38,2) + +\class["e_1" {below=0em,xshift=2pt}](38,4)\etasqclass(38,4) +\divfourclass["f_1" right](40,6) +\d3(38,4) % d_3(e_1) = h_2^2 n = h_1 t, see Bruner "A New Differential in the ASS" + +\tower(39,15){6}\classoptions["P^2i" {right=0em}](39,15) + +\class(38,18)\divfourclass["P^3d_0" {below left=0em}](38,18) +\etacubclass(38,16)\diveightclass["P^3e_0" {below=0em}](41,19) +\nustruct(38,18)\nustruct(38,17)\nustruct(38,16) +\etaclass(41,16)\divfourclass["P^2j" {below=0em}](42,17) +\d2(39,15)\d2(39,16) % d2(P^2i) = h_0 P^3d_0 +\d2(41,16,,1)\d2(42,17,,1) % d2(P^3e_0) = h_1^2 P^3d_0 +\d2(42,15)\d2(42,16) % d2(P^2j) = h_0 P^3e_0 + + + +\class["c_0 h_5" {below=-0.3em}](39,4)\etaclass(39,4) + +\d4(38,2,1,-1) \d4(38,3,1,-1) % d4(h_3h_5) = h_0x + + +\class(39,14) +\divfourclass["Pd_0e_0" {below=-0.2em}](39,14) +\etaclass(39,12) +\divfourclass["Pl" {below=0em}](40,13) +\d2(40,11)\d2(40,12) % d2(Pl) = h_0 P^2g +\d4(39,12)\d4(40,13,,-1) % d4(Pd_0e_0) = P^3d_0 + + + +\class["c_1g"](39,7) +\class["g^2"](40,8) +\class["u"](39,9)\etasqclass(39,9) +\divtwoclass["z"](41,11) +\class(41,5)\divfourclass["c_2"](41,5) +\class["v"](42,9) +\d2(42,9) % d2(v) = h_1^2 u + +\class["d_0^3"](42,12) + +\class["Ph_1h_5" {right=0em}](40,6)\etasqclass(40,6) +\divfourclass["Ph_2h_5" {right=0em}](42,8) + + +\class["P^4c_0"](40,18)\etaclass(40,18) + + +\class["P^5h_1"](41,20)\etasqclass(41,20) +\divfourclass["P^5h_2" right](43,22) + +\class(44,5)\divfourclass["g_2" below](44,5) +\etaclass(44,3) + +\class(44,18)\divfourclass["P^3g" left](44,18) +\etaclass(44,16)\divfourclass["P^2k" below](45,17) +\class["P^2r"](46,14) +\d2(45,15)\d2(45,16) % d2(P^2k) = h_0 P^3g +\d3(46,14)% d3(P^2r) = h0^2 P^2k +\class(45,4)\divtwoclass["h_4^3" below](45,4) + +\class(45,6)\divfourclass["h_5d_0" right](45,6) +\etaclass(45,4) + +\class["w"](45,9) + +\class["Pc_0g" left](45,12) +\d4(45,12) % d4(Pc_0g) = P^3g +\end{sseqdata} + +\printpage[name=S0ASS,page=0] + +\printpage[name=S0ASS,page=2] + +\printpage[name=S0ASS,page=3] + +\printpage[name=S0ASS,page=4] + +\begin{sseqpage}[name=S0ASS,page=5] +\structline[dashed,bend right=20](15,4)(16,7) +\structline[dashed](21,5)(22,8) +\structline[dashed,bend right=20](20,6)(23,9,-1) +\structline[dashed,bend right=20](23,6)(23,9,-1) +%\structline[dashed,bend right=20](32,6)(33,9) +%\structline[dashed,bend right=20](32,6)(33,9) +\classoptions["h_0^2i" left](23,9) +\classoptions["h_0^{10}h_5" left](31,11) +\classoptions["h_1h_5" below](32,2) +\classoptions["h_2h_5" below](34,2) +%\classoptions["h_0^2h_3h_5" {left=-0.1em}](38,4,1) +\classoptions["h_1h_3h_5" {below=-.4em}](39,3,1) +\classoptions["P^4h_3" {below=0em}](39,17) +\end{sseqpage} +\end{document}
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