
diff -r 4718e0696bc6 -r c27e875508fd text/evmap.tex
--- a/text/evmap.tex	Fri Jun 04 20:37:38 2010 -0700
+++ b/text/evmap.tex	Fri Jun 04 20:43:14 2010 -0700
@@ -41,7 +41,8 @@
 I lean toward the latter.}
 \medskip
 
-Before giving the proof, we state the essential technical tool of Lemma \ref{extension_lemma}, and then give an outline of the method of proof.
+Before giving the proof, we state the essential technical tool of Lemma \ref{extension_lemma}, 
+and then give an outline of the method of proof.
 
 Without loss of generality, we will assume $X = Y$.
 
@@ -50,7 +51,8 @@
 Let $f: P \times X \to X$ be a family of homeomorphisms (e.g. a generator of $CH_*(X)$)
 and let $S \sub X$.
 We say that {\it $f$ is supported on $S$} if $f(p, x) = f(q, x)$ for all
-$x \notin S$ and $p, q \in P$. Equivalently, $f$ is supported on $S$ if there is a family of homeomorphisms $f' : P \times S \to S$ and a `background'
+$x \notin S$ and $p, q \in P$. Equivalently, $f$ is supported on $S$ if 
+there is a family of homeomorphisms $f' : P \times S \to S$ and a `background'
 homeomorphism $f_0 : X \to X$ so that
 \begin{align*}
 	f(p,s) & = f_0(f'(p,s)) \;\;\;\; \mbox{for}\; (p, s) \in P\times S \\
@@ -313,7 +315,9 @@
 $G_*^{i,m}$.
 Choose a monotone decreasing sequence of real numbers $\gamma_j$ converging to zero.
 Let $\cU_j$ denote the open cover of $X$ by balls of radius $\gamma_j$.
-Let $h_j: CH_*(X)\to CH_*(X)$ be a chain map homotopic to the identity whose image is spanned by families of homeomorphisms with support compatible with $\cU_j$, as described in Lemma \ref{extension_lemma}.
+Let $h_j: CH_*(X)\to CH_*(X)$ be a chain map homotopic to the identity whose image is 
+spanned by families of homeomorphisms with support compatible with $\cU_j$, 
+as described in Lemma \ref{extension_lemma}.
 Recall that $h_j$ and also the homotopy connecting it to the identity do not increase
 supports.
 Define




