--- a/text/blobdef.tex	Mon Jul 19 15:56:09 2010 -0600
+++ b/text/blobdef.tex	Tue Jul 20 17:05:53 2010 -0700
@@ -134,12 +134,18 @@
 Equivalently, we can define a ball decomposition inductively. A ball decomposition of $X$ is a topological space $X'$ along with a pair of disjoint homeomorphic $n-1$-manifolds $Y \subset \bdy X$, so $X = X' \bigcup_Y \selfarrow$, and $X'$ is either a disjoint union of balls, or a topological space equipped with a ball decomposition.
 \end{defn}
 
+Even though our definition of a system of fields only associates vector spaces to $n$-manifolds, we can easily extend this to any topological space admitting a ball decomposition.
+\begin{defn}
+Given an $n$-dimensional system of fields $\cF$, its extension to a topological space $X$ admitting an $n$-ball decomposition is \todo{}
+\end{defn}
+\todo{This is well defined}
 
 Before describing the general case we should say more precisely what we mean by 
 disjoint and nested blobs.
-Disjoint will mean disjoint interiors.
-Nested blobs are allowed to coincide, or to have overlapping boundaries.
-Blob are allowed to intersect $\bd X$.
+Two blobs are disjoint if they have disjoint interiors.
+Nested blobs are allowed to have overlapping boundaries, or indeed to coincide.
+Blob are allowed to meet $\bd X$.
+
 However, we require of any collection of blobs $B_1,\ldots,B_k \subseteq X$ that
 $X$ is decomposable along the union of the boundaries of the blobs.
 \nn{need to say more here.  we want to be able to glue blob diagrams, but avoid pathological

--- a/text/intro.tex	Mon Jul 19 15:56:09 2010 -0600
+++ b/text/intro.tex	Tue Jul 20 17:05:53 2010 -0700
@@ -59,7 +59,7 @@
 topological $n$-category, and the complex $\CM{-}{T}$ of maps to a fixed target space $T$.
 
 In \S \ref{ss:ncat_fields}  we explain how to construct a system of fields from a topological $n$-category 
-(using a colimit along cellulations of a manifold), and in \S \ref{sec:ainfblob} give an alternative definition 
+(using a colimit along certain decompositions of a manifold into balls). With this in hand, we freely write $\bc_*(M; \cC)$ to indicate the blob complex of a manifold $M$ with the system of fields constructed from the $n$-category $\cC$. In \S \ref{sec:ainfblob} we give an alternative definition 
 of the blob complex for an $A_\infty$ $n$-category on an $n$-manifold (analogously, using a homotopy colimit).
 Using these definitions, we show how to use the blob complex to ``resolve" any topological $n$-category as an 
 $A_\infty$ $n$-category, and relate the first and second definitions of the blob complex.
@@ -207,17 +207,17 @@
 \label{property:functoriality}%
 The blob complex is functorial with respect to homeomorphisms.
 That is, 
-for a fixed $n$-dimensional system of fields $\cC$, the association
+for a fixed $n$-dimensional system of fields $\cF$, the association
 \begin{equation*}
-X \mapsto \bc_*(X; \cC)
+X \mapsto \bc_*(X; \cF)
 \end{equation*}
 is a functor from $n$-manifolds and homeomorphisms between them to chain 
 complexes and isomorphisms between them.
 \end{property}
-As a consequence, there is an action of $\Homeo(X)$ on the chain complex $\bc_*(X; \cC)$; 
+As a consequence, there is an action of $\Homeo(X)$ on the chain complex $\bc_*(X; \cF)$; 
 this action is extended to all of $C_*(\Homeo(X))$ in Theorem \ref{thm:evaluation} below.
 
-The blob complex is also functorial (indeed, exact) with respect to $\cC$, 
+The blob complex is also functorial (indeed, exact) with respect to $\cF$, 
 although we will not address this in detail here.
 
 \begin{property}[Disjoint union]
@@ -248,9 +248,9 @@
 \begin{property}[Contractibility]
 \label{property:contractibility}%
 With field coefficients, the blob complex on an $n$-ball is contractible in the sense that it is homotopic to its $0$-th homology.
-Moreover, the $0$-th homology of balls can be canonically identified with the vector spaces associated by the system of fields $\cC$ to balls.
+Moreover, the $0$-th homology of balls can be canonically identified with the vector spaces associated by the system of fields $\cF$ to balls.
 \begin{equation*}
-\xymatrix{\bc_*(B^n;\cC) \ar[r]^(0.4){\iso}_(0.4){\text{qi}} & H_0(\bc_*(B^n;\cC)) \ar[r]^(0.6)\iso & \cC(B^n)}
+\xymatrix{\bc_*(B^n;\cF) \ar[r]^(0.4){\iso}_(0.4){\text{qi}} & H_0(\bc_*(B^n;\cF)) \ar[r]^(0.6)\iso & \cF(B^n)}
 \end{equation*}
 \end{property}
 
@@ -268,10 +268,10 @@
 \begin{thm:skein-modules}[Skein modules]
 The $0$-th blob homology of $X$ is the usual 
 (dual) TQFT Hilbert space (a.k.a.\ skein module) associated to $X$
-by $\cC$.
+by $\cF$.
 (See \S \ref{sec:local-relations}.)
 \begin{equation*}
-H_0(\bc_*(X;\cC)) \iso A_{\cC}(X)
+H_0(\bc_*(X;\cF)) \iso A_{\cF}(X)
 \end{equation*}
 \end{thm:skein-modules}
 
@@ -469,5 +469,5 @@
 and
 Alexander Kirillov
 for many interesting and useful conversations. 
-During this work, Kevin Walker has been at Microsoft Station Q, and Scott Morrison has been at Microsoft Station Q and the Miller Institute for Basic Research at UC Berkeley.
+During this work, Kevin Walker has been at Microsoft Station Q, and Scott Morrison has been at Microsoft Station Q and the Miller Institute for Basic Research at UC Berkeley. We'd like to thank the Aspen Center for Physics for the conducive environment provided there during the final preparation of this manuscript.