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diff --git a/Master/texmf-dist/doc/latex/spectralsequences/examples/example_KUHFPSS.tex b/Master/texmf-dist/doc/latex/spectralsequences/examples/example_KUHFPSS.tex new file mode 100644 index 00000000000..7207b38a986 --- /dev/null +++ b/Master/texmf-dist/doc/latex/spectralsequences/examples/example_KUHFPSS.tex @@ -0,0 +1,92 @@ +%% +%% Package: spectralsequences.sty version 1.0 +%% Author: Hood Chatham +%% Email: hood@mit.edu +%% Date: 2017-06-18 +%% License: Latex Project Public License +%% +%% File: example_KUHFPSS.tex +%% +%% I think this is one of Eric Peterson's favorite spectral sequences, and his enthusiasm for it has rubbed off on me a bit. +%% Here our group is C_2 which acts on the periodicity element by -1, so again we have a norm element v in degree 2|G| = 4. +%% There are easier ways to understand this, but I explained the EO_3 one in terms of the comparison map from the ANSS, +%% and that's interesting here too. In the ANSS at 2, there is a differential d3(\alpha_3) = \alpha_1^4. Here a cobar calculation +%% shows that \alpha v = \alpha_3, so dividing the differential by \alpha gives d3(v) = \alpha_1^3. Now there's no Kudo differential +%% because the prime is 2, and the spectral sequence immediately collapses. +%% +%% Second, a demonstration of the falsehood of ku^{hC_2} = ko -- ku^{hC_2} has an extra generator as a ring, which is in degree -4. +%% In particular, it's not even connective. +%% + +\documentclass{article} +\usepackage[landscape,margin=2cm]{geometry} +\usepackage{spectralsequences} +\begin{document} +\sseqset{ + Z2class/.sseq style={circle,inner sep=0.3ex,fill=black}, + Zclass/.sseq style={fill=none,draw,inner sep=0.6ex}, + 2Zclass/.sseq style={fill=none,rectangle,draw,inner sep=0.6ex,outer sep=0.5ex} +} +\begin{sseqdata}[ + name=KRHFPSS, + x range={-12}{14}, + y range={0}{10}, + y axis style=center, + y axis gap=0.425cm, + tick step=4, + classes=Z2class, + differentials=->, + degree={-1}{#1-1}, + scale=0.85, + right clip padding=0.1cm, + top clip padding=0.05cm, + x axis extend start=0cm, + x axis extend end=0.33cm, + y axis extend end=0.3cm, +] + +\draw[background,xshift=-0.5cm,yshift=-0.51cm,step=1cm,gray,very thin] (\xmin+0.01,\ymin+0.01) grid (\xmax+0.9,\ymax+0.9); + +\pgfmathsetmacro\xitstart{int(int(\xmin/8)*8-16)} +\pgfmathsetmacro\xitgap{int(\xitstart+4)} +\pgfmathsetmacro\xitend{int(\xmax+2)} +\pgfmathsetmacro\xmaxpp{int(\xmax+2)} + +\foreach \x in {\xitstart,\xitgap,...,\xitend} { + \class[Zclass](\x,0) + \foreach \z in {0,...,\xmaxpp} { + \class(\x+\z+1,\z+1) + \structline(\x+\z,\z)(\x+\z+1,\z+1) + } +} + +\pgfmathsetmacro\xitstart{int(\xitgap)} +\pgfmathsetmacro\xitgap{int(\xitstart+8)} + +\foreach \x in {\xitstart,\xitgap,...,\xitend} { + \foreach\z in {0,...,\xmax}{ + \d4(\x+\z,\z) + } + \replaceclass[2Zclass](\x,0) +} +\end{sseqdata} +\printpage[name=KRHFPSS,page=0] +\newpage +\printpage[name=KRHFPSS,page=5] + + +\newpage +\begin{sseqpage}[name=KRHFPSS,page=0,keep changes] +\pgfmathsetmacro\antidiag{min(-\xmin,\ymax+0.8)} +\clip[background,xshift=0.28cm,yshift=-0.4cm](-\antidiag,\antidiag)--(-1,1)--(-0.4,0)--(\xmax+2,0)--(\xmax+2,\antidiag)--cycle; +\foreach \z in {2,6}{ + \doptions[draw=none]4(-\z-1,\z-1) + \structlineoptions[draw=none](-\z-1,\z-1)(-\z,\z) + \structlineoptions[draw=none](-\z-3,\z+1)(-\z-2,\z+2) + \replaceclass(-\z-2,\z+2) +} +\structlineoptions[draw=none](-3,1)(-2,2) +\end{sseqpage} +\newpage +\printpage[name=KRHFPSS,page=5] +\end{document}
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