--- a/text/evmap.tex Thu Aug 11 13:26:00 2011 -0700
+++ b/text/evmap.tex Thu Aug 11 13:54:38 2011 -0700
@@ -123,7 +123,7 @@
Let $g_j = f_1\circ f_2\circ\cdots\circ f_j$.
Let $g$ be the last of the $g_j$'s.
Choose the sequence $\bar{f}_j$ so that
-$g(B)$ is contained is an open set of $\cV_1$ and
+$g(B)$ is contained in an open set of $\cV_1$ and
$g_{j-1}(|f_j|)$ is also contained in an open set of $\cV_1$.
There are 1-blob diagrams $c_{ij} \in \bc_1(B)$ such that $c_{ij}$ is compatible with $\cV_1$
@@ -325,7 +325,7 @@
\end{proof}
For $S\sub X$, we say that $a\in \btc_k(X)$ is {\it supported on $S$}
-if there exists $a'\in \btc_k(S)$
+if there exist $a'\in \btc_k(S)$
and $r\in \btc_0(X\setmin S)$ such that $a = a'\bullet r$.
\newcommand\sbtc{\btc^{\cU}}
@@ -385,7 +385,7 @@
Now let $b$ be a generator of $C_2$.
If $\cU$ is fine enough, there is a disjoint union of balls $V$
on which $b + h_1(\bd b)$ is supported.
-Since $\bd(b + h_1(\bd b)) = s(\bd b) \in \bc_2(X)$, we can find
+Since $\bd(b + h_1(\bd b)) = s(\bd b) \in \bc_1(X)$, we can find
$s(b)\in \bc_2(X)$ with $\bd(s(b)) = \bd(b + h_1(\bd b))$ (by Corollary \ref{disj-union-contract}).
By Lemmas \ref{bt-contract} and \ref{btc-prod}, we can now find
$h_2(b) \in \btc_3(X)$, also supported on $V$, such that $\bd(h_2(b)) = s(b) - b - h_1(\bd b)$