--- 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.