# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1323730897 28800
# Node ID c57afb230bb1d977db0c687a870343713bb7b602
# Parent  bc4086c639b6b692c8085e2bb6133a1ae102c61a
remove lemma 3.2.3 (support-shrink lemma); it was only used once

diff -r bc4086c639b6 -r c57afb230bb1 blob to-do
--- a/blob to-do	Mon Dec 12 10:37:50 2011 -0800
+++ b/blob to-do	Mon Dec 12 15:01:37 2011 -0800
@@ -1,11 +1,9 @@
 
 ====== big ======
 
-* add "homeomorphism" spiel befure the first use of "homeomorphism in the intro
+* add "homeomorphism" spiel before the first use of "homeomorphism" in the intro
 * maybe also additional homeo warnings in other sections
 
-* Lemma 3.2.3 (\ref{support-shrink}) implicitly assumes embedded (non-self-intersecting) blobs. this can be fixed, of course, but it makes the argument more difficult to understand
-
 * Maybe give more details in 6.7.2
 
 
diff -r bc4086c639b6 -r c57afb230bb1 text/basic_properties.tex
--- a/text/basic_properties.tex	Mon Dec 12 10:37:50 2011 -0800
+++ b/text/basic_properties.tex	Mon Dec 12 15:01:37 2011 -0800
@@ -74,6 +74,9 @@
 For $y \in \bc_*(X)$ with $y = \sum c_i b_i$ ($c_i$ a non-zero number, $b_i$ a blob diagram),
 we define $\supp(y) \deq \bigcup_i \supp(b_i)$.
 
+%%%%% the following is true in spirit, but technically incorrect if blobs are not embedded; 
+%%%%% we only use this once, so move lemma and proof to Hochschild section
+\noop{ %%%%%%%%%% begin \noop
 For future use we prove the following lemma.
 
 \begin{lemma} \label{support-shrink}
@@ -94,6 +97,7 @@
 Both $f$ and the identity are compatible with $T$ (in the sense of acyclic models, \S\ref{sec:moam}), 
 so $f$ and the identity map are homotopic.
 \end{proof}
+} %%%%%%%%%%%%% end \noop
 
 For the next proposition we will temporarily restore $n$-manifold boundary
 conditions to the notation. Let $X$ be an $n$-manifold, with $\bd X = Y \cup Y \cup Z$.
diff -r bc4086c639b6 -r c57afb230bb1 text/hochschild.tex
--- a/text/hochschild.tex	Mon Dec 12 10:37:50 2011 -0800
+++ b/text/hochschild.tex	Mon Dec 12 15:01:37 2011 -0800
@@ -218,7 +218,10 @@
 to distance $\ep$ from *.
 (Move right or left so as to shrink the blob.)
 Extend to get a chain map $f: F_*^\ep \to F_*^\ep$.
-By Lemma \ref{support-shrink}, $f$ is homotopic to the identity.
+By Corollary \ref{disj-union-contract}, 
+$f$ is homotopic to the identity.
+(Use the facts that $f$ factors though a map from a disjoint union of balls
+into $S^1$, and that $f$ is the identity in degree 0.)
 Since the image of $f$ is in $J_*$, and since any blob chain is in $F_*^\ep$
 for $\ep$ sufficiently small, we have that $J_*$ is homotopic to all of $\bc_*(S^1)$.