<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%%
%% 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={-{&gt;[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&lt;\alpha_1,\alpha_1,\beta_1^3\right&gt;}" {below right=0em}](37,3)
\structline[dashed](37,3)(40,8)


\end{sseqpage}

\end{document} </pre></body></html>