
diff -r 352389c6ddcf -r edf8798ef477 text/a_inf_blob.tex
--- a/text/a_inf_blob.tex	Fri Aug 27 10:58:21 2010 -0700
+++ b/text/a_inf_blob.tex	Fri Aug 27 15:36:21 2010 -0700
@@ -12,19 +12,19 @@
 $\cl{\cC}(M)$ is homotopy equivalent to
 our original definition of the blob complex $\bc_*^\cD(M)$.
 
-\medskip
+%\medskip
 
-An important technical tool in the proofs of this section is provided by the idea of ``small blobs".
-Fix $\cU$, an open cover of $M$.
-Define the ``small blob complex" $\bc^{\cU}_*(M)$ to be the subcomplex of $\bc_*(M)$ 
-of all blob diagrams in which every blob is contained in some open set of $\cU$, 
-and moreover each field labeling a region cut out by the blobs is splittable 
-into fields on smaller regions, each of which is contained in some open set of $\cU$.
-
-\begin{thm}[Small blobs] \label{thm:small-blobs}
-The inclusion $i: \bc^{\cU}_*(M) \into \bc_*(M)$ is a homotopy equivalence.
-\end{thm}
-The proof appears in \S \ref{appendix:small-blobs}.
+%An important technical tool in the proofs of this section is provided by the idea of ``small blobs".
+%Fix $\cU$, an open cover of $M$.
+%Define the ``small blob complex" $\bc^{\cU}_*(M)$ to be the subcomplex of $\bc_*(M)$ 
+%of all blob diagrams in which every blob is contained in some open set of $\cU$, 
+%and moreover each field labeling a region cut out by the blobs is splittable 
+%into fields on smaller regions, each of which is contained in some open set of $\cU$.
+%
+%\begin{thm}[Small blobs] \label{thm:small-blobs}
+%The inclusion $i: \bc^{\cU}_*(M) \into \bc_*(M)$ is a homotopy equivalence.
+%\end{thm}
+%The proof appears in \S \ref{appendix:small-blobs}.
 
 \subsection{A product formula}
 \label{ss:product-formula}
@@ -69,7 +69,7 @@
 
 Let $G_*\sub \bc_*(Y\times F;C)$ 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 Proposition \ref{thm:small-blobs} that $\bc_*(Y\times F; C)$ 
+It follows from Lemma \ref{thm:small-blobs} that $\bc_*(Y\times F; C)$ 
 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.)
@@ -309,7 +309,7 @@
 
 The image of $\psi$ is the subcomplex $G_*\sub \bc(X)$ generated by blob diagrams which split
 over some decomposition of $J$.
-It follows from Proposition \ref{thm:small-blobs} that $\bc_*(X)$ is homotopic to 
+It follows from Lemma \ref{thm:small-blobs} that $\bc_*(X)$ is homotopic to 
 a subcomplex of $G_*$. 
 
 Next we define a map $\phi:G_*\to \cT$ using the method of acyclic models.




