
diff -r f58d590e8a08 -r e47dcbf119e7 text/a_inf_blob.tex
--- a/text/a_inf_blob.tex	Thu Jun 24 14:20:38 2010 -0400
+++ b/text/a_inf_blob.tex	Thu Jun 24 14:21:20 2010 -0400
@@ -17,11 +17,7 @@
 
 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 $\cU$. 
-\nn{KW: We need something a little stronger: Every blob diagram (even a 0-blob diagram) is splittable into pieces which are small w.r.t.\ $\cU$.
-If field have potentially large coupons/boxes, then this is a non-trivial constraint.
-On the other hand, we could probably get away with ignoring this point.
-Maybe the exposition will be better if we sweep this technical detail under the rug?}
+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.
 
 \begin{thm}[Small blobs] \label{thm:small-blobs}
 The inclusion $i: \bc^{\cU}_*(M) \into \bc_*(M)$ is a homotopy equivalence.




