diff --git a/resources/MayConcise/ConciseRevised.pdf b/resources/MayConcise/ConciseRevised.pdf index 34946b5..f17fd9d 100644 Binary files a/resources/MayConcise/ConciseRevised.pdf and b/resources/MayConcise/ConciseRevised.pdf differ diff --git a/resources/MayConcise/ConciseRevised.tex b/resources/MayConcise/ConciseRevised.tex index 254b8d1..8183b9a 100644 --- a/resources/MayConcise/ConciseRevised.tex +++ b/resources/MayConcise/ConciseRevised.tex @@ -1,9 +1,39 @@ +\def\OPTpagesize{4.8in,7.9in} % Page size +\def\OPTtopmargin{0.4in} % Margin at the top of the page +\def\OPTbottommargin{0.4in} % Margin at the bottom of the page +\def\OPTinnermargin{0.2in} % Margin on the inner side of the page +\def\OPTbindingoffset{0.0in} % Extra offset on the inner side +\def\OPToutermargin{0.2in} % Margin on the outer side of the page +\def\OPTcoverwidth{4.75in} % width of text on cover page +\def\OPTcoverheight{7.85in} % height of text on cover page +\def\OPTlinkcolor{0,0.45,0} % RGB components for clickable links + \documentclass{amsbook} +\usepackage{etex} \usepackage{amssymb, amsfonts, lacromay} +\usepackage[ + papersize={\OPTpagesize}, + top=\OPTtopmargin, + bottom=\OPTbottommargin, + inner=\OPTinnermargin, + outer=\OPToutermargin, +]{geometry} + +\usepackage[ + backref=page, + colorlinks, + citecolor=linkcolor, + linkcolor=linkcolor, + urlcolor=linkcolor, + unicode, +]{hyperref} + \usepackage[v2]{xy} +\PassOptionsToPackage{table}{xcolor} +\usepackage{xcolor} % For colored cells in tables we need \cellcolor - +\definecolor{linkcolor}{rgb}{\OPTlinkcolor} %\makeindex %theoremstyle{plain} --- default @@ -52,6 +82,12 @@ %\renewcommand{\thechapter}{\arabic{chapter}} + +\newlength{\coverheight} +\setlength{\coverheight}{\OPTcoverheight} +\newlength{\coverwidth} +\setlength{\coverwidth}{\OPTcoverwidth} + \title{A Concise Course in Algebraic Topology} \author{J. P. May} @@ -8289,7 +8325,7 @@ Let $M$ be a compact connected $n$-manifold with boundary $\pa M$, where $n\ge \item Prove: if $M$ is contractible, then $\pa M$ has the homology of a sphere. \item Assume that $M$ is orientable. Let $n = 2m+1$ and let $K$ be the kernel of the homomorphism $H_m(\pa M) \rtarr H_m(M)$ induced by the inclusion, where homology is taken -with coefficients in a field. Prove: $\dimÊÊ\,H_m(\pa M)Ê=Ê2\dimÊÊ\,K$. +with coefficients in a field. Prove: $\dim��\,H_m(\pa M)�=�2\dim��\,K$. \end{enumerate} Let $n = 3$ in the rest of the problems.