%%
%% Package: spectralsequences v1.3.3 2023-01-28
%% Author: Hood Chatham
%% Email:
[email protected]
%% Date: 2023-01-28
%% License: Latex Project Public License
%%
%% File: example_unstable_ASS_SO.tex
%%
%% From Kathryn Lesh: A conjecture on the unstable Adams spectral sequences for SO and U top of page 21.
%%
http://hopf.math.purdue.edu//Lesh/uass-so-model.pdf
%%
\documentclass{spectralsequence-example}
\begin{document}
\sseqset{
M3M2/.sseq style = { fill },
M4M3/.sseq style = { circlen = 2, fill }
}
%\pgfkeys{/sseqpages/class/M4M3/.show code}
\NewSseqCommand \tower { O{} d() } {
\IfNoValueF{#2}{\class(#2)}
\savestack
\begin{scope}[#1]
\DoUntilOutOfBounds{
\class(\lastx,\lasty+1)
\structline(\lastclass1)(\lastclass)
}
\end{scope}
\restorestack
}
\NewSseqCommand \etaclass {} {
\class(\lastx+1,\lasty+1)
\structline(\lastclass1)(\lastclass)
}
\NewSseqCommand \divtwoclass {} {
\class(\lastx,\lasty-1)
\structline(\lastclass1)(\lastclass)
}
\begin{sseqdata}[ name = SO_UASS, tick step = 5, x range = {0}{20}, Adams grading, y range={0}{10} ]
\class(1,0)
\tower(3,0)
\begin{scope}[M3M2]
\tower(7,0)
\etaclass\etaclass
\tower(11,3)
\class(14,4)
\divtwoclass\divtwoclass
\etaclass\etaclass\etaclass
\divtwoclass\divtwoclass
\class(16,5)\etaclass
\end{scope}
\begin{scope}[M4M3]
\tower(15,0)
\etaclass\etaclass\etaclass
\divtwoclass\divtwoclass
\end{scope}
\d2(15,0)\d2(15,1)\d2(15,2)
\d2(16,1)\d2(17,2)\d2(18,3)
\d2(18,2)\d2(18,1)
\end{sseqdata}
\printpage[ name = SO_UASS, page = 2 ]
\newpage
\printpage[ name = SO_UASS, page = 3 ]
\end{document}
