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example_K(F3,n).tex
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example_K(F3,n).tex
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\documentclass{article}
\usepackage[margin=0.2in,top=0.4in,landscape]{geometry}
\usepackage{sseqpages}
\usepackage{amssymb}
\def\Z{\mathbb{Z}}
\begin{document}
\sseqnewclasspattern{vertical}{
(0,0);
(0,-0.2)(0,0.2);
(0,-0.4)(0,0)(0,0.4)
}
\begin{sseqdata}[name=K(Z/3;2),cohomological Serre grading,classes={draw=none},xscale=2.2,yscale=1.5,right clip padding=20pt, x range={0}{8},x axis gap=20pt,
class placement transform={scale=1.2}, class pattern=vertical,
title={Page \page},
x label={$H^*(K(\Z/3,2),\Z/3)$},
y label={$H^*(K(\Z/3,1),\Z/3)$},
]
\class["1"](0,0)
\class["\alpha"](0,1)
\class["x"](0,2)
\class["\alpha x"](0,3)
\class["x^2"](0,4)
\class["\alpha x^2"](0,5)
\class["x^3"](0,6)
\class["\iota_2"](2,0)
\class["\alpha\iota_2"](2,1)
\class["x\iota_2"](2,2)
\class["\alpha x\iota_2"](2,3)
\class["x^2\iota_2"](2,4)
\class["\alpha x^2\iota_2"](2,5)
\class["x^3\iota_2"](2,6)
\class["\beta\iota_2"](3,0)
\class["\alpha\beta\iota_2"](3,1)
\class["x\beta\iota_2"](3,2)
\class["\alpha x\beta\iota_2"](3,3)
\class["x^2\beta\iota_2"](3,4)
\class["\alpha x^2"](3,5)
\class["x^3\beta\iota_2"](3,6)
\class["\iota_2^2"](4,0)
\class["\alpha\iota_2^2"](4,1)
\class["x\iota_2^2"](4,2)
\class["\alpha x\iota_2^2"](4,3)
\class["x^2\iota_2^2"](4,4)
\class["\alpha x^2\iota_2^2"](4,5)
\class["x^3\iota_2^2"](4,6)
\class["\iota_2\beta\iota_2"](5,0)
\class["\alpha\iota_2\beta\iota_2"](5,1)
\class["x\iota_2\beta\iota_2"](5,2)
\class["\alpha x\iota_2\beta\iota_2"](5,3)
\class["x^2\iota_2\beta\iota_2"](5,4)
\class["\alpha x^2\iota_2\beta\iota_2"](5,5)
\class["x^3\iota_2\beta\iota_2"](5,6)
\class["\iota_2^3"](6,0)
\class["\alpha\iota_2^3"](6,1)
\class["x\iota_2^3"](6,2)
\class["\alpha x\iota_2^3"](6,3)
\class["x^2\iota_2^3"](6,4)
\class["\alpha x^2\iota_2^3"](6,5)
\class["x^3\iota_2^3"](6,6)
\class["\iota_2^2\beta\iota_2"](7,0)
\class["\alpha a"](7,1)
\class["xa"](7,2)
\class["\alpha xa"](7,3)
\class["x^2a"](7,4)
\class["\alpha x^2a"](7,5)
\class["x^3a"](7,6)
\class["P^1\beta\iota_2"](7,0)
\class["\alpha b"](7,1)
\class["x b"](7,2)
\class["\alpha x b"](7,3)
\class["x^2 b"](7,4)
\class["\alpha x^2 b"](7,5)
\class["x^3 b"](7,6)
\class["\iota_2^4"](8,0)
\class["\alpha c"](8,1)
\class["x c"](8,2)
\class["\alpha x c"](8,3)
\class["x^2 c"](8,4)
\class["\alpha x^2 c"](8,5)
\class["x^3 c"](8,6)
\class["\beta P^1\beta\iota_2"](8,0)
\class["\alpha d"](8,1)
\class["x d"](8,2)
\class["\alpha x d"](8,3)
\class["x^2 d"](8,4)
\class["\alpha x^2 d"](8,5)
\class["x^3 d"](8,6)
\class(9,0)\class(9,0)
\class(9,1)
\class(9,2)
\class(9,3)
\class(9,4)
\class(9,5)
\class(10,0)\class(10,0)\class(10,0)
\class(10,2)\class(10,2)
\class(10,4)\class(10,4)
\class(11,0)\class(11,0)
\class(11,2)
\class(12,0)
\class(13,0)
\class(14,0)
\class(15,0)
%\class["(\beta\iota_2)^2"](6,0)
\d2(0,1) %d2(a)=i
\d3(0,2) %d3(x) = b(i)
\d2(0,3) % d2(ax) = ix
\d3(0,4) % d2(x^2) = xb(i)
\d2(0,5) % d2(ax^2) = ix^2
%\d7
\d2(2,1) % d2(ai) = i^2
\d2(2,3) % d2(axi) = xi^2
\d2(2,5) % d2(ax^2i)=x^2i^2)
\d2(3,1) % d2(abi)=ib(i)
\d2(3,3)
\d2(3,5)
\d2(4,1) % d2(ai^2)=i^3
\d2(4,3)
\d2(4,5)
\d2(5,1,,1) %d2(ai_2bi_2) = i_2^2 bi_2
\d2(5,3,,1)
\d2(5,5,,1)
\d2(6,1,,1) %d2(ai_2^3) = i_2^4
\d2(6,3,,1)
\d2(6,5,,1)
\d2(7,1,1) % d2(ai_2^2bi_2) = i_2^3 bi_2
\d2(7,3,1)
\d2(7,5,1)
\d2(7,1,2) % d2(aP^1bi_2) = i_2 P^1bi_2
\d2(7,3,2)
\d2(7,5,2)
\d3(7,2,2) % d3(x P^1bi_2) = bi_2 P^1bi_2
\d3(7,4,2)
\d2(8,1,1,2) % d2(a i_2^4) = i_2^5
\d2(8,3,1,2)
\d2(8,5,1,2)
\d2(8,1,2,2) % d2(a bP^1bi_2) = i_2 bP^1bi_2
\d2(8,3,2,2)
\d2(8,5,2,2)
\d3(8,2,2) % d3(x bP^1bi_2) = bi_2 bP^1bi_2
\d3(8,4,2)
\d5(3,4,,2) % d5(x^2i_2) = bP^1bi_2 -- Kudo differential
\d7(0,6,,2) % d7(x^3) = P^1bi_2
\d7(2,6,,2)
\d7(3,6,,3)
\d7(4,6,,2)
\d7(5,6)
\d7(6,6)
\d7(7,6,1)
\d7(7,6,2)
\d7(8,6,1)
\d7(8,6,2)
\end{sseqdata}
\printpage[name=K(Z/3;2),page=2]
\newpage
\printpage[name=K(Z/3;2),page=3]
\newpage
\printpage[name=K(Z/3;2),page=5]
\newpage
\printpage[name=K(Z/3;2),page=6]
\newpage
\printpage[name=K(Z/3;2),page=7]
\newpage
\begin{sseqpage}[name=K(Z/3;2), page=0, no differentials, y range={-1}{0}, y axis extend end = 40pt, x axis gap =50pt,y axis gap=30pt, yscale = 1.5,
no labels, no y ticks, no title
]
\begin{scope}[background]
\node[anchor=west] at (-2,0) { H^*(K(\Z/3,2),\Z/3)};
\node[anchor=west] at (-2,-1) { H^*(K(\Z/3,2),\Z)};
\end{scope}
\draw[->] (2,0) to[bend left=30, "\beta^1"] (3,0);
\draw[->] (4,0) to[bend left=30, "\beta^1"] (5,0);
\draw[->] (6,0) to[bend right=30, "\beta^2"'] (7,0,1);
\draw[->] (7,0,2) to[bend left=30, "\beta"] (8,0,2);
\draw[->] (8,0,1) to[bend right=30, "\beta^1"'] (9,0);
\class["\Z\{1\}"](0,-1)
\class["\Z/3\{\beta\iota_3\}"](2,-1)
\class["\Z/3\{\beta\iota_2^2\}"](5,-1)
\class["\Z/9\{\beta\iota_2^3\}"](7,-1)
\class["\Z/3\{\beta P^1\iota_2\}"](8,-1)
\end{sseqpage}
\newpage
\begin{sseqdata}[name=K(Z/3;3),cohomological Serre grading,classes={draw=none},xscale=2.2,yscale=1.7,y axis gap=40pt,x axis gap=30pt, x range={0}{9},
class pattern = vertical, class placement transform = {scale=1.6},
title={Page \page},
x label={$H^*(K(\Z/3,2),\Z/3)$},
y label={$H^*(K(\Z/3,1),\Z/3)$},
]
\class["1"](0,0)
\class["\iota_2"](0,2)
\class["\beta\iota_2"](0,3)
\class["\iota_2^2"](0,4)
\class["\iota_2\beta\iota_2"](0,5)
\class["\iota_2^3"](0,6)
\class["P^1\beta\iota_2"](0,7)
\class["\iota_2^2\beta\iota_2"](0,7)
\class["\beta P^1\beta\iota_2"](0,8)
\class["\iota_2^4"](0,8)
\class["\iota_3"](3,0)
\class["\iota_2\iota_3"](3,2)
\class["\beta\iota_2\iota_3"](3,3)
\class["\iota_2^2\iota_3"](3,4)
\class["\iota_2\beta\iota_2\iota_3"](3,5)
\class["\iota_2^3\iota_3"](3,6)
\class["\beta\iota_3"](4,0)
\class["\iota_2\beta\iota_3"](4,2)
\class["\beta\iota_2\beta\iota_3"](4,3)
\class["P^1\iota_3"](7,0)
\class["\iota_3\beta\iota_3"](7,0)
\class["\beta P^1\iota_3"](8,0)
\class["(\beta\iota_3)^2"](8,0)
\class["P^1\beta\iota_3"](8,0)
\class["\beta P^1\beta\iota_3"](9,0)
\d3(0,2)
\d4(0,3)
\d3(0,4)
\d3(0,5)
\d7(0,6,,1)
\d3(0,7,2)
\d8(0,7,1,3)
\d3(0,8,2)
\d9(0,8,1)
\d5(3,4,,1)
\d3(4,2,,2)
\d4(4,3,,2)
\end{sseqdata}
\printpage[name=K(Z/3;3),page=3]
\newpage
\printpage[name=K(Z/3;3),page=4]
\newpage
\printpage[name=K(Z/3;3),page=5]
\newpage
\printpage[name=K(Z/3;3),page=7]
\newpage
\printpage[name=K(Z/3;3),page=9]
\newpage
\begin{sseqpage}[name=K(Z/3;3), page=0, no differentials, y range={-1}{0}, y axis extend end = 40pt, x axis extend end=40pt, x axis gap =50pt, yscale = 1.5,
no labels, no y ticks, no title
]
\begin{scope}[background]
\node[anchor=west] at (-2.2,0) { H^*(K(\Z/3,3),\Z/3)};
\node[anchor=west] at (-2.2,-1) { H^*(K(\Z/3,3),\Z)};
\end{scope}
\draw[->] (3,0) to[bend left=30, "\beta^1"] (4,0);
\draw[->] (7,0,1) to[bend right=30, "\beta^1"'] (8,0,1);
\draw[->] (7,0,2) to[bend left=30, "\beta^1"] (8,0,2);
\draw[->] (8,0,3) to[bend left=30, "\beta^1"] (9,0);
\class["\Z\{1\}"](0,-1)
\class["\Z/3\{\beta\iota_3\}"](4,-1)
\class["\Z/3\{\beta P^1\iota_3\}"](8,-1)
\class["\Z/3\{\beta(\iota_3\beta\iota_3)\}"](8,-1)
\class["\Z/3\{\beta P^1\beta\iota_3\}"](9,-1)
\end{sseqpage}
\begin{sseqdata}[name=K(Z/3;4),cohomological Serre grading,classes={draw=none},xscale=2,yscale=1.5,y axis gap=20pt,x axis gap=30pt, x range={0}{10},
class pattern = vertical, class placement transform = {scale=1.6}
]
\begin{scope}[background,page constraint = {\page>0} ]
\node at (0.5*\xmax + 0.5*\xmin,\ymax + 1) { \textup{Page \page}};
\node[rotate=90] at (-1.2,0.5*\ymax + 0.5*\ymin) {H^*(K(\Z/3,3),\Z/3)};
\node at (0.5*\xmax + 0.5*\xmin, \ymin-2) {K(\Z/3,4)};
\end{scope}
\class["1"](0,0)
\class["\iota_3"](0,3)
\class["\beta\iota_3"](0,4)
\class["P^1\iota_3"](0,7)
\class["\beta P^1\iota_3"](0,8)
\class["\iota_3\beta\iota_3"](0,7)
\class["(\beta\iota_3)^2"](0,8)
\class["P^1\beta\iota_3"](0,8)
\class["\beta P^1\beta\iota_3"](0,9)
\class["\iota_4"](4,0)
\class["\iota_3\iota_4"](4,3)
\class["\beta\iota_3\iota_4"](4,4)
\class["\beta\iota_4"](5,0)
\class["\iota_3\beta\iota_4"](5,3)
\class["\beta\iota_3\beta\iota_4"](5,4)
\class["\iota_4^2"](8,0)
\class["P^1\iota_4"](8,0)
\class["\iota_4 \beta\iota_4"](9,0)
\class["P^1\beta\iota_4"](9,0)
\class["\beta P^1\iota_4"](9,0)
\class["\beta P^1\beta\iota_4"](10,0)
\d4(0,3) % d4(i_3) = i_4
\d4(0,7,2)
\d4(4,3,,1)
\d4(5,3,,1)
\d5(0,4)
\d8(0,7,1,2)
\d9(0,8,1,2)
\d5(0,8,2)
\d9(0,8,3,3)
\d10(0,9)
%\d
\end{sseqdata}
\printpage[name=K(Z/3;4),page=4]
\newpage
\printpage[name=K(Z/3;4),page=5]
\newpage
\printpage[name=K(Z/3;4),page=8]
\newpage
\printpage[name=K(Z/3;4),page=9]
\newpage
\printpage[name=K(Z/3;4),page=10]
\newpage
\begin{sseqpage}[name=K(Z/3;4), page=0, no differentials, y range={-1}{0}, y axis extend end = 40pt, x axis extend end=40pt, x axis gap =50pt, yscale = 1.5, no labels,
no y ticks]
\begin{scope}[background]
\node[anchor=west] at (-2.2,0) { H^*(K(\Z/3,4),\Z/3)};
\node[anchor=west] at (-2.2,-1) { H^*(K(\Z/3,4),\Z)};
\end{scope}
\draw[->] (4,0) to[bend left=30, "\beta"] (5,0);
\draw[->] (8,0,1) to[bend right=30, "\beta"] (9,0,1);
\draw[->] (8,0,2) to[bend left=30, "\beta"] (9,0,3);
\draw[->] (9,0,2) to[ "\beta"] (10,0);
\class["\Z\{1\}"](0,-1)
\class["\Z/3\{\beta\iota_4\}"](5,-1)
\class["\Z/3\{\beta P^1\iota_4\}"](9,-1)
\class["\Z/3\{\beta(\iota_4^2)\}"](9,-1)
\class["\Z/3\{\beta P^1\beta\iota_4\}"](10,-1)
\end{sseqpage}
\end{document}