# HG changeset patch
# User Scott Morrison <scott@tqft.net>
# Date 1277403638 14400
# Node ID f58d590e8a088576d0b7273528bea1f37a0bb53f
# Parent  1bb33e217a5ace3b01dc5504003e6c153894c43b
cross-references for the small blobs lemma

diff -r 1bb33e217a5a -r f58d590e8a08 text/appendixes/smallblobs.tex
--- a/text/appendixes/smallblobs.tex	Thu Jun 24 10:17:19 2010 -0400
+++ b/text/appendixes/smallblobs.tex	Thu Jun 24 14:20:38 2010 -0400
@@ -15,15 +15,9 @@
 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 
+This follows from Remark \ref{rem:for-small-blobs} 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}
-[...]
-}
-
 
 \begin{proof}[Proof of Theorem \ref{thm:small-blobs}]
 We begin by describing the homotopy inverse in small degrees, to illustrate the general technique.
diff -r 1bb33e217a5a -r f58d590e8a08 text/evmap.tex
--- a/text/evmap.tex	Thu Jun 24 10:17:19 2010 -0400
+++ b/text/evmap.tex	Thu Jun 24 14:20:38 2010 -0400
@@ -621,15 +621,16 @@
 
 \nn{this should perhaps be a numbered remark, so we can cite it more easily}
 
-\begin{rem}
-For the proof of xxxx below we will need the following observation on the action constructed above.
+\begin{rem*}
+\label{rem:for-small-blobs}
+For the proof of Lemma \ref{lem:CH-small-blobs} 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 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}
+\end{rem*}