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diff --git a/Master/texmf-dist/doc/latex/spectralsequences/examples/ASS-S_2.tex b/Master/texmf-dist/doc/latex/spectralsequences/examples/ASS-S_2.tex new file mode 100644 index 00000000000..67be3dd6b57 --- /dev/null +++ b/Master/texmf-dist/doc/latex/spectralsequences/examples/ASS-S_2.tex @@ -0,0 +1,399 @@ +%% +%% Description: Adams Novikov Spectral Sequence for $S_2$ +%% +%% +%% 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{spectralsequence-example} + + +\begin{document} +\sseqset{imJ/.sseq style={purple}} + + +\NewSseqCommand\twoclass{O{}d()}{ + \IfNoValueF{#2}{\pushstack(#2)} + \class[#1](\lastx,\lasty+1) + \structline(\lastclass1)(\lastclass) +} + +\NewSseqCommand\divtwoclass{O{}d()}{ + \IfNoValueF{#2}{\pushstack(#2)} + \class[#1](\lastx,\lasty-1) + \structline(\lastclass1)(\lastclass) +} + + +\NewSseqCommand\etaclass{O{}d()}{ + \IfNoValueF{#2}{\pushstack(#2)} + \class[#1](\lastx+1,\lasty+1) + \structline(\lastclass1)(\lastclass) +} +\NewSseqCommand\divetaclass{O{}d()}{ + \IfNoValueF{#2}{\pushstack(#2)} + \class[#1](\lastx-1,\lasty-1) + \structline(\lastclass1)(\lastclass) +} +\NewSseqCommand\etastruct{d()}{ + \IfNoValueF{#1}{\pushstack(#1)} + \structline(\lastx-1,\lasty-1,-1)(\lastclass) +} + + +\NewSseqCommand\nuclass{O{}d()}{ + \IfNoValueF{#2}{\pushstack(#2)} + \class[#1](\lastx+3,\lasty+1) + \structline(\lastclass1)(\lastclass) +} + +\NewSseqCommand\nustruct{d()}{ + \IfNoValueF{#1}{\pushstack(#1)} + \structline(\lastx-3,\lasty-1,-1)(\lastclass) +} + +\NewSseqCommand\hznudiamond{d()}{ + \IfNoValueF{#1}{\pushstack(#1)} + \savestack + \class(\lastx,\lasty+1) + \structline(\lastclass1)(\lastclass) + \nustruct + \restorestack +} + +\NewSseqCommand\etanudiamond{d()}{ + \IfNoValueF{#1}{\pushstack(#1)} + \savestack + \class(\lastx+1,\lasty+1) + \structline(\lastclass1)(\lastclass) + \nustruct + \restorestack +} + +\NewSseqCommand \czero {O{} r() }{ + \savestack + \class[#1](#2) + \etaclass + \restorestack +} + +\NewSseqCommand\tower {O{}d()mO{}} { + \begin{scope}[#4] + \IfNoValueF{#2}{\class[#1](#2)} + \savestack + \Do{#3-1}{ + \class(\lastx, \lasty+1) + \structline(\lastclass)(\lastclass1) + } + \restorestack + \end{scope} +} + + +\NewSseqCommand \towergroup {o r() m O{}} { + \tower(#2){#3}[#4] + \IfNoValueF{#1}{\classoptions[#1](#2)} + \etaclass\etaclass\etaclass + \nustruct\divtwoclass\nustruct\divtwoclass + \nustruct\nuclass +} + + +\protected\def\Psqvphant{\vphantom{P^2}} +\NewSseqGroup \Phone { mm } { + \class["#1h_1#2"](0,0) + \etaclass\etaclass + \divtwoclass\divtwoclass["\Psqvphant#1h_2#2" {below=-4pt}] +} + +\NewSseqGroup \Phonegroup {G{}}{ + \sseqset{class label handler = { \sseqnormalizemonomial{##1} }} + \czero["#1c_0" above](-1,-2) + \Phone[imJ]{P#1}{} + \nuclass[imJ]\divtwoclass[imJ]\divtwoclass["#1d_0" left,name=d0] + \etaclass\etaclass\etaclass + \nustruct\divtwoclass\nustruct\divtwoclass\nustruct\divtwoclass["#1e_0" left,name=e0] + \nuclass\hznudiamond + \divtwoclass + \classoptions["#1g" {below=0.3em},page=0-3](\lastclass) + %\etanudiamond + + % Have to go back and draw path e0 to g + \savestack + \d2(e0,-1) + \etaclass(e0)\d2(\lastclass,-1) + \divtwoclass[name=f0]\d2(\lastclass,-1) + \nuclass[name=nuf0] + \etastruct % Now we're back at g + \restorestack + \nuclass[name=nug]\hznudiamond\nuclass[name=nu2g] +} + + +\NewSseqGroup \Phonegroupb {G{}}{ + \Phonegroup{P#1} + + \divtwoclass["\Psqvphant#1j" {below left=-1pt,yshift=2pt}](f0) \d2(\lastclass,-1) + \divtwoclass(nuf0) \d2(\lastclass,-1) + \nustruct\divtwoclass["\Psqvphant#1k" {below=-1pt}] \d2(\lastclass,-1) + \nuclass\d2(\lastclass,-1) + \hznudiamond + \divtwoclass["\Psqvphant#1l" {below left=-1pt,yshift=2pt}]\d2(\lastclass,-1) + \nuclass\d2(\lastclass,-1)\hznudiamond + \divtwoclass["\Psqvphant#1m" {below left=-3pt},name=m] + + \divtwoclass(nug)\structline(\lastclass)(\lastx+1,\lasty+1) + \divtwoclass(nu2g)\nustruct + \divtwoclass\structline(\lastclass)(\lastx+1,\lasty+1) + \d2(m,-1) +} + + + +\begin{sseqdata}[ + name = ASS-S_2, + Adams grading, + classes=fill, + class labels={above left=0.2em,black}, + x range={0}{46}, + y range={0}{23}, + % xscale=0.7, + % yscale=0.8, + differentials = blue, + classes = { tooltip = { (\xcoord,\ycoord) } }, + grid = go, + run off = - +] +\towergroup(0,0){\ymax-\ymin+2} +\classoptions["h_2" below](3,1) +\nuclass +\divetaclass\divetaclass["h_3" below] +\tower{4} + + +\Phonegroup(9,5) +\classoptions["f_0"](f0) + +\Phonegroupb(17,9) +\pushstack(d0) +\tower["i" {below left,yshift=2pt}](23,7){6}[imJ] +\structline(\lastclass)(\lastx+3,\lasty+1,-1) +\structline(\lastx,\lasty+1)(\lastx+3,\lasty+2,-1) +\d2(23,7) +\d2(23,8) + +\Phonegroupb(25,13){P} +\Phonegroupb(33,17){P^2} +\tower["P^2i" {below left,yshift=2pt}](39,15){6}[imJ] +\structline(\lastclass)(\lastx+3,\lasty+1,-1) +\structline(\lastx,\lasty+1)(\lastx+3,\lasty+2,-1) +\d2(39,15) +\d2(39,16) +\d4(39,12) +\d4(40,13,,1) + +\Phonegroup(41,21){P^4} +\tower["P^2i" {below left,yshift=2pt}](47,19){6}[imJ] +\d2(47,19) +\d2(47,20) + +\towergroup["h_4" below](15,1){8}[imJ] +\classoptions["h_3^3" below](\lastclass) + +\tower["h_3^2" left](14,2){2} +\d2(15,1) % d2(h_4) = h_0h_3^2 +\d3(15,2)\d3(15,3) % d2(h_0h_4) = h_0d_0 + +\class["c_1"](19,3)\nuclass +\czero["h_4c_0"](23,4) + + + +\towergroup["h_5" below](31,1){16}[imJ] +\nuclass +\divetaclass\divetaclass["h_3h_5" {below=-2pt}] +\tower{4} + +\class["n"{above=-0.5pt}](31,5) +\nuclass\nuclass +\divetaclass["t"] +\nuclass["c_1g"] + +\class["q" {below right=-0.7pt}](32,6) +\etaclass + +\class["p"](33,4) +\twoclass\divetaclass["d_1"] +\nuclass\nuclass +\divetaclass["x" below]\tower{6} + +\d[bend left=15]4(38,3,,2) +\d[bend left=30]4(38,2) + + +\tower["h_4^2" below](30,2){4} +\etaclass +\tower["r" left](30,6){6} +\d3(\lastclass) + +\d2(31,1)\d2(31,2)\d2(31,3) +\d3(31,4)\d3(31,5)\d3(31,6)\d3(31,7)\d3(31,8,-1) +\d4(31,8,1)\d4(32,9,,1) +\d4(31,9,-1,-1)\d4(31,10,-1,-1) + +\d3(34,2) + + +\class(38,6)\d2(\lastclass,-1) +\twoclass\d2(\lastclass,-1) +\twoclass\nustruct\d2(\lastclass,-1) +\twoclass\nustruct\d4(\lastclass,-1) +\divetaclass["e_0g"]\d4(\lastclass,-1) + +\czero[pin distance=3em,pin=below right:h_5c_0"](39,4) + +\class["e_1" {below=-1pt}](38,4) +\d3(\lastclass,1) +\etaclass\etaclass\divtwoclass\divtwoclass["f_1" below] +\etaclass +\divtwoclass\d2(\lastclass) +\divtwoclass\d2(\lastclass,-1) + + +\Phone(40,6){P}{h_5} + +\class["u"](39,9)\etaclass\etaclass\divtwoclass + +\class["g^2"](40,8) +\class["v"](42,9) +\d2(\lastclass) + +\tower["P^2r" {below=-4pt}](46,14){6} +\d3(\lastclass) + +\class["Pe_0g" right](45,12) +\d4(\lastclass) + +\class["w"](45,9) + +\class["d_0r" right](44,10) +\d3(\lastclass) + + +\class["h_4^3" below](45,3)\twoclass + +\tower["h_5d_0" {below right=-2pt}](45,5){3} +\etaclass\etaclass +\nuclass(45,5)\hznudiamond +\nustruct(45,7) + +\tower["g_2" below](44,4){3} +\etaclass + +\class["N"](46,8) +\class["gj"](46,11) + +\tower(47,13){12} +\foreach \y in {13,...,18} { \d2(47,\y)} +\end{sseqdata} +\centering + +\begin{sseqpage}[ + page=7, + name=ASS-S_2, Adams grading, + class labels={below}, + %label distance=-1pt, + below label distance=0pt, + differentials=blue, + x range={0}{40}, + y range={0}{10}, + xscale=0.7, + yscale=1.7, + grid=go, + right clip padding=2em +] +\structline[dashed,bend right=20](15,4)(16,7,1) +\structline[dashed,bend right=20](23,9,2)(24,11) +\structline[dashed,bend right=20](31,11)(32,15) +\structline[dashed,bend right=20](39,17,2)(40,19) + +\structline[dashed](14,2)(15,5,1) +\structline[dashed](21,5)(22,8) +\structline[dashed,bend right=20](20,6)(23,9,1) +\structline[dashed](23,6)(23,9,1) +\structline[dashed,bend right=20](30,2)(33,4) +\structline[dashed,bend left=20](32,6)(35,9) + +\structline[dashed](38,4)(39,7) + +\structline[dashed](40,8)(40,10) +\structline[dashed](40,8)(41,10) +\structline[dashed,bend left=40](39,9)(42,12) +\structline[dashed](41,10)(42,12) + +\classoptions["h_0^2i" right=1pt](23,9) +\classoptions["h_0^{10}h_5" left](31,11) +\classoptions["h_1h_5" below](32,2) +\classoptions["h_0h_2h_5" below](34,3) +\classoptions["h_2^2h_5" below](37,3) +\classoptions["h_0^2h_3h_5" {left=-0.1em}](38,4,1) +\classoptions["h_1h_3h_5" {below=-.4em}](39,3,1) + +\classoptions["Ph_3" left](15,5,1) +\classoptions["P^2h_3" left](23,9,1) +%\classoptions["P^3h_3" left](31,13,1) +%\classoptions["P^4h_3" left](39,17,1) +\end{sseqpage} +%\end{document} + +\newgeometry{margin = 0.1cm} +\printpage[name=ASS-S_2,page=2,xscale=0.7,yscale=0.8,keep changes] + +%\printpage[name=ASS-S_2,page=2] + +\printpage[name=ASS-S_2,page=3] + +\printpage[name=ASS-S_2,page=4] + +\begin{sseqpage}[name=ASS-S_2,page=5] +\structline[dashed,bend right=20](15,4)(16,7,1) +\structline[dashed,bend right=20](23,9,2)(24,11) +\structline[dashed,bend right=20](31,11)(32,15) +\structline[dashed,bend right=20](39,17,2)(40,19) + +\structline[dashed](14,2)(15,5,1) +\structline[dashed](21,5)(22,8) +\structline[dashed,bend right=20](20,6)(23,9,1) +\structline[dashed](23,6)(23,9,1) +\structline[dashed,bend right=20](30,2)(33,4) +\structline[dashed,bend left=20](32,6)(35,9) + +\structline[dashed](38,4)(39,7) + +\structline[dashed](40,8)(40,10) +\structline[dashed](40,8)(41,10) +\structline[dashed,bend left=40](39,9)(42,12) +\structline[dashed](41,10)(42,12) + +\classoptions["g" {below=0.3em}](20,4) +\classoptions["{d_0^2=Pg=c_0g}" {xshift=5pt, below=-2.15em}](28,8) + + +\classoptions["h_0^2i" right=1pt](23,9) +\classoptions["h_0^{10}h_5" left](31,11) +\classoptions["h_1h_5" below](32,2) +\classoptions["h_0h_2h_5" below](34,3) +\classoptions["h_2^2h_5" below](37,3) +\classoptions["h_0^2h_3h_5" {left=-0.1em}](38,4,1) +\classoptions["h_1h_3h_5" {below=-.4em}](39,3,1) + +\classoptions["Ph_3" left](15,5,1) +\classoptions["P^2h_3" left](23,9,1) +%\classoptions["P^3h_3" left](31,13,1) +%\classoptions["P^4h_3" left](39,17,1) +\end{sseqpage} +\end{document}
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