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+%%
+%% Description: The homotopy fixed point spectral sequence for $C_2$ acting on $KU$ by complex conjugation, compare the odd-primary case HFPSS-EO2_3
+%%
+%% File: example_KUHFPSS.tex
+%%
+%% 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{spectralsequence-example}
+\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 type=center,
+ y axis gap=0.425cm,
+ tick step=4,
+ classes=Z2class,
+ differentials=->,
+ degree={-1}{#1-1},
+ scale=1.45,
+ 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,
+ grid=go
+]
+
+% This is just to make sure the bounding box doesn't move around
+\path[background] (\xmin-1,\ymin-1) rectangle (\xmax+1,\ymax+1);
+
+\def\xmin{-12}
+\def\xmax{14}
+\sseqparseint\xitstart{\xmin/8*8-16} % division is integer division (I think with rounding towards 0...) so /8*8 rounds up to the nearest multiple of 8?
+\sseqparseint\xitgap{\xitstart+4}
+\sseqparseint\xitend{\xmax+2}
+\sseqparseint\xmaxpp{\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)
+ }
+}
+
+\sseqparseint\xitstart{\xitgap}
+\sseqparseint\xitgap{\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]
+\def\xmin{-12}\def\xmax{14}
+\pgfmathsetmacro\antidiag{min(-\xmin,\ymax+0.8)}
+\clip[background,xshift=0.2cm,yshift=-0.33cm](-\antidiag,\antidiag)--(-1,1)--(-0.4,0)--(\xmax + 0.28,0)--(\xmax+0.28,\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} \ No newline at end of file