
diff -r 0a578230ee21 -r 0bf2002737f0 text/evmap.tex
--- a/text/evmap.tex	Thu Dec 08 23:13:56 2011 -0800
+++ b/text/evmap.tex	Fri Dec 09 17:01:53 2011 -0800
@@ -50,7 +50,7 @@
 \medskip
 
 If $b$ is a blob diagram in $\bc_*(X)$, recall from \S \ref{sec:basic-properties} that the {\it support} of $b$, denoted
-$\supp(b)$ or $|b|$, to be the union of the blobs of $b$.
+$\supp(b)$ or $|b|$, is the union of the blobs of $b$.
 %For a general $k$-chain $a\in \bc_k(X)$, define the support of $a$ to be the union
 %of the supports of the blob diagrams which appear in it.
 More generally, we say that a chain $a\in \bc_k(X)$ is supported on $S$ if
@@ -64,14 +64,14 @@
 $f$ is supported on $Y$.
 
 If $f: M \cup (Y\times I) \to M$ is a collaring homeomorphism
-(cf. end of \S \ref{ss:syst-o-fields}),
+(cf.\ the end of \S \ref{ss:syst-o-fields}),
 we say that $f$ is supported on $S\sub M$ if $f(x) = x$ for all $x\in M\setmin S$.
 
 \medskip
 
 Fix $\cU$, an open cover of $X$.
 Define the ``small blob complex" $\bc^{\cU}_*(X)$ to be the subcomplex of $\bc_*(X)$ 
-of all blob diagrams in which every blob is contained in some open set of $\cU$, 
+generated by blob diagrams such that every blob is contained in some open set of $\cU$, 
 and moreover each field labeling a region cut out by the blobs is splittable 
 into fields on smaller regions, each of which is contained in some open set of $\cU$.
 
@@ -114,7 +114,7 @@
 The composition of all the collar maps shrinks $B$ to a ball which is small with respect to $\cU$.
 
 Let $\cV_1$ be an auxiliary open cover of $X$, subordinate to $\cU$ and 
-fine enough that a condition stated later in the proof is satisfied.
+fine enough that a condition stated later in this proof is satisfied.
 Let $b = (B, u, r)$, with $u = \sum a_i$ the label of $B$, and $a_i\in \bc_0(B)$.
 Choose a sequence of collar maps $\bar{f}_j:B\cup\text{collar}\to B$ satisfying conditions 
 specified at the end of this paragraph.
@@ -426,7 +426,7 @@
 \eq{
     e_{XY} : \CH{X \to Y} \otimes \bc_*(X) \to \bc_*(Y) ,
 }
-well-defined up to (coherent) homotopy,
+well-defined up to coherent homotopy,
 such that
 \begin{enumerate}
 \item on $C_0(\Homeo(X \to Y)) \otimes \bc_*(X)$ it agrees with the obvious action of 




