diff -r 77a80b7eb98e -r bb48ee2ecf9e text/appendixes/moam.tex --- a/text/appendixes/moam.tex Thu Oct 06 12:20:35 2011 -0700 +++ b/text/appendixes/moam.tex Thu Oct 06 12:27:38 2011 -0700 @@ -2,6 +2,9 @@ \section{The method of acyclic models} \label{sec:moam} +In this section we recall the method of acyclic models for the reader's convenience. The material presented here is closely modeled on \cite[Chapter 4]{MR0210112}. +We use this method throughout the paper (c.f. Lemma \ref{support-shrink}, Theorem \ref{thm:product}, Theorem \ref{thm:gluing} and Theorem \ref{thm:map-recon}), as it provides a very convenient way to show the existence of a chain map with desired properties, even when many non-canonical choices are required in order to construct one, and further to show the up-to-homotopy uniqueness of such maps. + Let $F_*$ and $G_*$ be chain complexes. Assume $F_k$ has a basis $\{x_{kj}\}$ (that is, $F_*$ is free and we have specified a basis).