# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1277255109 25200
# Node ID b1da2a454ee76c579aeffea917ed353a1a3ad163
# Parent  2df1284ab09e846999b30f902d5794e3d1d5308a
refinement of ev map statement needed for small blobs

diff -r 2df1284ab09e -r b1da2a454ee7 text/appendixes/smallblobs.tex
--- a/text/appendixes/smallblobs.tex	Mon Jun 21 15:28:02 2010 -0700
+++ b/text/appendixes/smallblobs.tex	Tue Jun 22 18:05:09 2010 -0700
@@ -15,10 +15,14 @@
 We can't quite do the same with all $\cV_k$ just equal to $\cU$, but we can get by if we give ourselves arbitrarily little room to maneuver, by making the blobs we act on slightly smaller.
 \end{rem}
 \begin{proof}
+This follows from the remark \nn{number it and cite it?} following the proof of 
+Proposition \ref{CHprop}.
+\end{proof}
+\noop{
 We choose yet another open cover, $\cW$, which so fine that the union (disjoint or not) of any one open set $V \in \cV$ with $k$ open sets $W_i \in \cW$ is contained in a disjoint union of open sets of $\cU$.
 Now, in the proof of Proposition \ref{CHprop}
-\todo{I think I need to understand better that proof before I can write this!}
-\end{proof}
+[...]
+}
 
 
 \begin{proof}[Proof of Theorem \ref{thm:small-blobs}]
diff -r 2df1284ab09e -r b1da2a454ee7 text/evmap.tex
--- a/text/evmap.tex	Mon Jun 21 15:28:02 2010 -0700
+++ b/text/evmap.tex	Tue Jun 22 18:05:09 2010 -0700
@@ -618,7 +618,6 @@
 \end{proof}
 
 
-\noop{
 
 \nn{this should perhaps be a numbered remark, so we can cite it more easily}
 
@@ -626,11 +625,13 @@
 For the proof of xxxx below we will need the following observation on the action constructed above.
 Let $b$ be a blob diagram and $p:P\times X\to X$ be a family of homeomorphisms.
 Then we may choose $e$ such that $e(p\ot b)$ is a sum of generators, each
-of which has support arbitrarily close to $p(t,|b|)$ for some $t\in P$.
-This follows from the fact that the 
-\nn{not correct, since there could also be small balls far from $|b|$}
+of which has support close to $p(t,|b|)$ for some $t\in P$.
+More precisely, the support of the generators is contained in a small neighborhood
+of $p(t,|b|)$ union some small balls.
+(Here ``small" is in terms of the metric on $X$ that we chose to construct $e$.)
 \end{rem}
-}
+
+
 
 \begin{prop}
 The $CH_*(X, Y)$ actions defined above are associative.