# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1298007472 28800
# Node ID e412b47640d1a45e73e24c61d3e6b100c74f53c3
# Parent  f8add4477ca2f0848a951405b3bd4a0cbf0eb1e1
clarified what's small and what's not in the proof of the small blob lemma for BT_*

diff -r f8add4477ca2 -r e412b47640d1 text/evmap.tex
--- a/text/evmap.tex	Mon Feb 14 09:14:26 2011 +1100
+++ b/text/evmap.tex	Thu Feb 17 21:37:52 2011 -0800
@@ -346,8 +346,9 @@
 
 It suffices to show that we can deform a finite subcomplex $C_*$ of $\btc_*(X)$ into $\sbtc_*(X)$
 (relative to any designated subcomplex of $C_*$ already in $\sbtc_*(X)$).
-The first step is to replace families of general blob diagrams with families that are 
-small with respect to $\cU$.
+The first step is to replace families of general blob diagrams with families 
+of blob diagrams that are small with respect to $\cU$.
+(If $f:P \to \BD_k$ is the family then for all $p\in P$ we have that $f(p)$ is a diagram in which the blobs are small.)
 This is done as in the proof of Lemma \ref{small-blobs-b}; the technique of the proof works in families.
 Each such family is homotopic to a sum families which can be a ``lifted" to $\Homeo(X)$.
 That is, $f:P \to \BD_k$ has the form $f(p) = g(p)(b)$ for some $g:P\to \Homeo(X)$ and $b\in \BD_k$.