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%%
%% Description: Adams Novikov Spectral Sequence for $S_3$
%%
%% File: example_anss3.tex
%%
%% Draws the Adams Novikov spectral sequence at the prime 3 through the 45 stem.
%% In this range, all we see is the Toda differential d_{2p-1}(\beta_{p/p}) = \alpha\beta^p
%% Thanks to Eric Peterson for contributing this diagram. Presumably he copied it from page 13 of the green book.
%% Compare this to page 5 of example_ass3
%%
\documentclass[tooltips]{spectralsequence-example}
\begin{document}
% tower definitions
\NewSseqCommand\alphaclass{d()}{
\IfNoValueTF{#1}{}{\pushstack(#1)}
\class(\lastx+3,\lasty+1)
\structline(\lastclass)(\lastclass1)
}
\NewSseqCommand\betaclass{d()}{
\IfNoValueTF{#1}{}{\pushstack(#1)}
\class(\lastx+7,\lasty+1)
\structline(\lastclass)(\lastclass1)
}
\centering
\begin{sseqpage}[
Adams grading,
classes = { tooltip = {(\xcoord,\ycoord)}, inner sep=1.2pt },
class labels = below,
label distance=3pt,
differentials={-{>[width=4]}, target anchor=-60},
y range={0}{11},
x range={0}{45},
x tick step=5,
xscale=0.7,
yscale=1.2,
y axis gap=2em
]
\class[rectangle,fill,inner sep=3pt](0,0)
\class["\alpha_1"](3,1) \structline(0,0)(3,1)
\class["\alpha_2"](7,1)
\class[circlen=2,"\alpha_{3/2}"](11,1)
\class["\alpha_4"](15,1)
\class["\alpha_5"](19,1)
\class[circlen=2,"\alpha_{6/2}"](23,1)
\class["\alpha_7"](27,1)
\class["\alpha_8"](31,1)
\class[circlen=3,"\alpha_{9/3}"](35,1)
\class["\alpha_{10}"](39,1)
\class["\alpha_{11}"](43,1)
\class["\beta_1"](10,2) \structline(3,1)(10,2)
\class["\beta_2" left](26,2)
\class["\beta_{3/3}" left](34,2)
\class["\beta_{3/2}" {left}](38,2)
\class["\beta_3" left](42,2)
% tower off of beta_1
\alphaclass(10,2)\betaclass
\alphaclass\betaclass
\alphaclass\betaclass
\alphaclass\betaclass
% tower off of beta_2
\alphaclass(26,2)\betaclass
\alphaclass\betaclass
\alphaclass
% tower off of beta_3/3
\alphaclass(34,2)\betaclass
\alphaclass\betaclass
% tower off of beta_3
\class[fill,circlen=2](45,3) \structline(42,2,-1)(45,3,-1)
\betaclass
% d5s
\d5(34,2)
\d5(44,4)
%% Doug's contributions
\classoptions["{\left<\alpha_1,\alpha_1,\beta_1^3\right>}" {below right=0em}](37,3)
\structline[dashed](37,3)(40,8)
\end{sseqpage}
\end{document}
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