--- a/text/basic_properties.tex	Sun Feb 06 18:31:17 2011 -0800
+++ b/text/basic_properties.tex	Sun Feb 06 20:54:10 2011 -0800
@@ -31,16 +31,16 @@
 conditions to the notation.
 
 Suppose that for all $c \in \cC(\bd B^n)$
-we have a splitting $s: H_0(\bc_*(B^n, c)) \to \bc_0(B^n; c)$
+we have a splitting $s: H_0(\bc_*(B^n; c)) \to \bc_0(B^n; c)$
 of the quotient map
-$p: \bc_0(B^n; c) \to H_0(\bc_*(B^n, c))$.
+$p: \bc_0(B^n; c) \to H_0(\bc_*(B^n; c))$.
 For example, this is always the case if the coefficient ring is a field.
 Then
 \begin{prop} \label{bcontract}
-For all $c \in \cC(\bd B^n)$ the natural map $p: \bc_*(B^n, c) \to H_0(\bc_*(B^n, c))$
+For all $c \in \cC(\bd B^n)$ the natural map $p: \bc_*(B^n; c) \to H_0(\bc_*(B^n; c))$
 is a chain homotopy equivalence
-with inverse $s: H_0(\bc_*(B^n, c)) \to \bc_*(B^n; c)$.
-Here we think of $H_0(\bc_*(B^n, c))$ as a 1-step complex concentrated in degree 0.
+with inverse $s: H_0(\bc_*(B^n; c)) \to \bc_*(B^n; c)$.
+Here we think of $H_0(\bc_*(B^n; c))$ as a 1-step complex concentrated in degree 0.
 \end{prop}
 \begin{proof}
 By assumption $p\circ s = \id$, so all that remains is to find a degree 1 map
@@ -67,8 +67,13 @@
 This follows from Properties \ref{property:disjoint-union} and \ref{property:contractibility}.
 \end{proof}
 
-Recall the definition of the support of a blob diagram as the union of all the 
-blobs of the diagram.
+%Recall the definition of the support of a blob diagram as the union of all the 
+%blobs of the diagram.
+We define the {\it support} of a blob diagram $b$, $\supp(b) \sub X$, 
+to be the union of the blobs of $b$.
+For $y \in \bc_*(X)$ with $y = \sum c_i b_i$ ($c_i$ a non-zero number, $b_i$ a blob diagram),
+we define $\supp(y) \deq \bigcup_i \supp(b_i)$.
+
 For future use we prove the following lemma.
 
 \begin{lemma} \label{support-shrink}

--- a/text/blobdef.tex	Sun Feb 06 18:31:17 2011 -0800
+++ b/text/blobdef.tex	Sun Feb 06 20:54:10 2011 -0800
@@ -33,9 +33,11 @@
 to define fields on these pieces.
 
 We of course define $\bc_0(X) = \cF(X)$.
-(If $X$ has nonempty boundary, instead define $\bc_0(X; c) = \cF(X; c)$ for each $c \in \cF(\bdy X)$.
+In other words, $\bc_0(X)$ is just the vector space of all fields on $X$.
+
+(If $X$ has nonempty boundary, instead define $\bc_0(X; c) = \cF(X; c)$ for $c \in \cF(\bdy X)$.
+The blob complex $\bc_*(X; c)$ will depend on a fixed boundary condition $c\in \cF(\bdy X)$.
 We'll omit such boundary conditions from the notation in the rest of this section.)
-In other words, $\bc_0(X)$ is just the vector space of all fields on $X$.
 
 We want the vector space $\bc_1(X)$ to capture 
 ``the space of all local relations that can be imposed on $\bc_0(X)$".
@@ -148,8 +150,8 @@
 \item For any (possibly empty) configuration of blobs on an $n$-ball $D$, we can add
 $D$ itself as an outermost blob.
 (This is used in the proof of Proposition \ref{bcontract}.)
-\item If $X'$ is obtained from $X$ by gluing, then any permissible configuration of blobs
-on $X$ gives rise to a permissible configuration on $X'$.
+\item If $X\sgl$ is obtained from $X$ by gluing, then any permissible configuration of blobs
+on $X$ gives rise to a permissible configuration on $X\sgl$.
 (This is necessary for Proposition \ref{blob-gluing}.)
 \end{itemize}
 Combining these two operations can give rise to configurations of blobs whose complement in $X$ is not
@@ -166,8 +168,8 @@
 \end{align*}
 Here $A \cup B = [0,1] \times [-1,1] \times [0,1]$ and $C \cup D = [-1,0] \times [-1,1] \times [0,1]$. 
 Now, $\{A\}$ is a valid configuration of blobs in $A \cup B$, 
-and $\{C\}$ is a valid configuration of blobs in $C \cup D$, 
-so we must allow $\{A, C\}$ as a configuration of blobs in $[-1,1]^2 \times [0,1]$. 
+and $\{D\}$ is a valid configuration of blobs in $C \cup D$, 
+so we must allow $\{A, D\}$ as a configuration of blobs in $[-1,1]^2 \times [0,1]$. 
 Note however that the complement is not a manifold.
 \end{example}
 
@@ -244,7 +246,7 @@
 \label{defn:blobs}
 The $k$-th vector space $\bc_k(X)$ of the \emph{blob complex} of $X$ is the direct sum over all 
 configurations of $k$ blobs in $X$ of the vector space of $k$-blob diagrams with that configuration, 
-modulo identifying the vector spaces for configurations that only differ by a permutation of the balls 
+modulo identifying the vector spaces for configurations that only differ by a permutation of the blobs 
 by the sign of that permutation. 
 The differential $\bc_k(X) \to \bc_{k-1}(X)$ is, as above, the signed sum of ways of 
 forgetting one blob from the configuration, preserving the field $r$:
@@ -263,11 +265,6 @@
 is immediately obvious from the definition.
 A homeomorphism acts in an obvious way on blobs and on fields.
 
-We define the {\it support} of a blob diagram $b$, $\supp(b) \sub X$, 
-to be the union of the blobs of $b$.
-For $y \in \bc_*(X)$ with $y = \sum c_i b_i$ ($c_i$ a non-zero number, $b_i$ a blob diagram),
-we define $\supp(y) \deq \bigcup_i \supp(b_i)$.
-
 \begin{remark} \label{blobsset-remark} \rm
 We note that blob diagrams in $X$ have a structure similar to that of a simplicial set,
 but with simplices replaced by a more general class of combinatorial shapes.

--- a/text/tqftreview.tex	Sun Feb 06 18:31:17 2011 -0800
+++ b/text/tqftreview.tex	Sun Feb 06 20:54:10 2011 -0800
@@ -456,10 +456,10 @@
 %$\bc_0(X) = \lf(X)$.
 \begin{defn}
 \label{defn:TQFT-invariant}
-The TQFT invariant of $X$ associated to a system of fields $\cF$ and local relations $\cU$ is 
+The TQFT invariant of $X$ associated to a system of fields $\cC$ and local relations $U$ is 
 	$$A(X) \deq \lf(X) / U(X),$$
-where $\cU(X) \sub \lf(X)$ is the space of local relations in $\lf(X)$:
-$\cU(X)$ is generated by fields of the form $u\bullet r$, where
+where $U(X) \sub \lf(X)$ is the space of local relations in $\lf(X)$:
+$U(X)$ is generated by fields of the form $u\bullet r$, where
 $u\in U(B)$ for some embedded $n$-ball $B\sub X$ and $r\in \cC(X\setmin B)$.
 \end{defn}
 The blob complex, defined in the next section,