# HG changeset patch
# User Scott Morrison <scott@tqft.net>
# Date 1309373495 25200
# Node ID 36bfe7c2eecc223d3f5123551d8292a974e30a6c
# Parent  91f2efaf938fda8832835b4ebfd653d0cc673a70
using consistent names for field in \S 7

diff -r 91f2efaf938f -r 36bfe7c2eecc text/a_inf_blob.tex
--- a/text/a_inf_blob.tex	Wed Jun 29 10:44:13 2011 -0700
+++ b/text/a_inf_blob.tex	Wed Jun 29 11:51:35 2011 -0700
@@ -8,10 +8,10 @@
 
 We will show below 
 in Corollary \ref{cor:new-old}
-that when $\cC$ is obtained from a system of fields $\cD$ 
+that when $\cC$ is obtained from a system of fields $\cE$ 
 as the blob complex of an $n$-ball (see Example \ref{ex:blob-complexes-of-balls}), 
 $\cl{\cC}(M)$ is homotopy equivalent to
-our original definition of the blob complex $\bc_*(M;\cD)$.
+our original definition of the blob complex $\bc_*(M;\cE)$.
 
 %\medskip
 
@@ -51,7 +51,7 @@
 
 First we define a map 
 \[
-	\psi: \cl{\cC_F}(Y) \to \bc_*(Y\times F;C) .
+	\psi: \cl{\cC_F}(Y) \to \bc_*(Y\times F;\cE) .
 \]
 On 0-simplices of the hocolimit 
 we just glue together the various blob diagrams on $X_i\times F$
@@ -60,7 +60,7 @@
 For simplices of dimension 1 and higher we define the map to be zero.
 It is easy to check that this is a chain map.
 
-In the other direction, we will define a subcomplex $G_*\sub \bc_*(Y\times F;C)$
+In the other direction, we will define a subcomplex $G_*\sub \bc_*(Y\times F;\cE)$
 and a map
 \[
 	\phi: G_* \to \cl{\cC_F}(Y) .
@@ -69,9 +69,9 @@
 Given a decomposition $K$ of $Y$ into $k$-balls $X_i$, let $K\times F$ denote the corresponding
 decomposition of $Y\times F$ into the pieces $X_i\times F$.
 
-Let $G_*\sub \bc_*(Y\times F;C)$ be the subcomplex generated by blob diagrams $a$ such that there
+Let $G_*\sub \bc_*(Y\times F;\cE)$ be the subcomplex generated by blob diagrams $a$ such that there
 exists a decomposition $K$ of $Y$ such that $a$ splits along $K\times F$.
-It follows from Lemma \ref{thm:small-blobs} that $\bc_*(Y\times F; C)$ 
+It follows from Lemma \ref{thm:small-blobs} that $\bc_*(Y\times F; \cE)$ 
 is homotopic to a subcomplex of $G_*$.
 (If the blobs of $a$ are small with respect to a sufficiently fine cover then their
 projections to $Y$ are contained in some disjoint union of balls.)