text/appendixes/smallblobs.tex
changeset 402 853376c08d76
parent 396 f58d590e8a08
child 405 2e1b1efbf928
--- a/text/appendixes/smallblobs.tex	Sat Jun 26 17:22:53 2010 -0700
+++ b/text/appendixes/smallblobs.tex	Sun Jun 27 12:28:06 2010 -0700
@@ -7,7 +7,7 @@
 
 \begin{lem}
 \label{lem:CH-small-blobs}
-Fix an open cover $\cU$, and a sequence $\cV_k$ of open covers which are each strictly subordinate to $\cU$. For a given $k$, consider $\cG_k$ the subspace of $C_k(\Homeo(M)) \tensor \bc_*(M)$ spanned by $f \tensor b$, where $f:P^k \times M \to M$ is a $k$-parameter family of homeomorphisms such that for each $p \in P$, $f(p, -)$ makes $b$ small with respect to $\cV_k$. We can choose an up-to-homotopy representative $\ev$ of the chain map of Property \ref{property:evaluation} which gives the action of families of homeomorphisms, which restricts to give a map
+Fix an open cover $\cU$, and a sequence $\cV_k$ of open covers which are each strictly subordinate to $\cU$. For a given $k$, consider $\cG_k$ the subspace of $C_k(\Homeo(M)) \tensor \bc_*(M)$ spanned by $f \tensor b$, where $f:P^k \times M \to M$ is a $k$-parameter family of homeomorphisms such that for each $p \in P$, $f(p, -)$ makes $b$ small with respect to $\cV_k$. We can choose an up-to-homotopy representative $\ev$ of the chain map of Theorem \ref{thm:evaluation} which gives the action of families of homeomorphisms, which restricts to give a map
 $$\ev : \cG_k \subset C_k(\Homeo(M)) \tensor \bc_*(M) \to \bc^{\cU}_*(M)$$
 for each $k$.
 \end{lem}