%% %% Description: The Serre spectral sequence for $\HZ$ cohomology of $\CP^\infty \to pt \to K(\Z,3)$ %% %% File: example_KZ3.tex %% %% This was one of the first spectral sequences I ever worked out (probably after the one for loops S^n), in the summer of 2013 with Kevin Donoghue. %% \documentclass{article} \usepackage[landscape,margin=0.5cm,top=2cm]{geometry} \usepackage{spectralsequences} \usepackage{amssymb} \def\Z{\mathbb{Z}} % Last time test: 1.1 sec \begin{document} \def\column#1[#2]{\foreach \y in {0,...,6} {\class[#2](#1,2*\y)}} \sseqset{classes={draw=none}} \begin{sseqdata}[ name={K(Z,3)}, x range={0}{12}, y range={0}{10}, cohomological Serre grading, differentials={->}, xscale=1.8, y axis gap=0.7cm, math nodes, x axis extend end=0.8cm, this page cycles=red, title=\textup{Serre SS Page \page{}}, x label = {$H^*(K(\Z,3))$}, y label = {$H^*(K(\Z,2))$} ] \column0["\Z\{\ifnum\y>0\relax x\ifnum\y>1\relax ^{\y}\fi\else1\fi\}"] \column3["\Z\{a\ifnum\y>0x\ifnum\y>1 ^{\y}\fi\fi\}"] \foreach\y in {1,...,6} {\d["\cdot \y"']3(0,2*\y)} \replaceclass["\Z/3"](3,4) \replaceclass["\Z/5"](3,8) \column6["\Z/2"] \d3(3,2) \d3(3,6) \d3(3,10) \replaceclass["\Z/2"](3,6) \replaceclass["\Z/3"](3,10) \column8["\Z/3"] \d5(3,4) \d5(3,10) \column9["\Z/2"] \d3(6,2) \d3(6,6) \d3(6,10) \column10["\Z/2"] \d7(3,6) \column11["\Z/3"] \d3(8,2) \d3(8,4) \d3(8,8) \d3(8,10) \column12["\Z/2\oplus\Z/5"] \column13["\Z/2"] \column15["\Z/2\oplus\Z/2\oplus\Z/5"] \d3(9,2) \d3(9,6) \d3(9,10) \d3(10,2) \d3(10,6) \d3(10,10) \d3(10,12) \d3(12,2) \d3(12,4) \d3(12,6) \d3(12,8) \d3(12,10) \d3(12,4) \replaceclass["\Z/5"](12,0) \replaceclass["\Z/5"](12,4) \replaceclass["\Z/5"](12,8) \d9(3,8) \replaceclass["\Z/5"](12,10) \replaceclass["\Z/2"](15,0) \replaceclass["\Z/2\oplus\Z/2"](15,4) \d5(10,4) \class["\Z/3"](16,0) \class["\Z/3"](16,6) \d5(11,4) \d5(11,10) \class["\Z/2"] (17,0) \class["\Z/2"](17,8) \d5(12,12) \class["\Z/2"](19,0) \d9(10,8) \class["\Z/5"](23,0) \d11(12,10) \replaceclass["\Z/6"](16,0) \d13(3,12) %\replaceclass["\Z/6"](21,0) %\d13(8,12) \class["\Z/3"](24,0) \d13(11,12) \end{sseqdata} \printpage[name={K(Z,3)}, page=0,no differentials] \newpage \printpage[name={K(Z,3)}, page=0] \newpage \printpage[name={K(Z,3)}, page=3] \newpage \printpage[name={K(Z,3)}, page=5] \newpage \printpage[name={K(Z,3)}, page=7] \newpage \printpage[name={K(Z,3)}, page=9] \newpage \printpage[name={K(Z,3)}, page=11] \newpage \printpage[name={K(Z,3)}, page=12] \end{document}