--- a/text/a_inf_blob.tex	Tue Sep 21 07:37:41 2010 -0700
+++ b/text/a_inf_blob.tex	Tue Sep 21 14:44:17 2010 -0700
@@ -282,7 +282,7 @@
 or $M\to Y$, instead of an undecorated colimit with fancier $k$-categories over $Y$.
 Information about the specific map to $Y$ has been taken out of the categories
 and put into sphere modules and decorations.
-\nn{...}
+\nn{just say that one could do something along these lines}
 
 %Let $F \to E \to Y$ be a fiber bundle as above.
 %Choose a decomposition $Y = \cup X_i$
@@ -442,9 +442,4 @@
 It is now easy to see that $\psi\circ\phi$ is the identity on the nose.
 Another acyclic models argument shows that $\phi\circ\psi$ is homotopic to the identity.
 (See the proof of Theorem \ref{thm:product} for more details.)
-\end{proof}
-
-\nn{maybe should also mention version where we enrich over
-spaces rather than chain complexes;}
-
-
+\end{proof}
\ No newline at end of file

--- a/text/appendixes/famodiff.tex	Tue Sep 21 07:37:41 2010 -0700
+++ b/text/appendixes/famodiff.tex	Tue Sep 21 14:44:17 2010 -0700
@@ -234,8 +234,6 @@
 
 \medskip
 
-\nn{need to clean up references from the main text to the lemmas of this section}
-
 %%%%%% Lo, \noop{...}
 \noop{
 

--- a/text/appendixes/moam.tex	Tue Sep 21 07:37:41 2010 -0700
+++ b/text/appendixes/moam.tex	Tue Sep 21 14:44:17 2010 -0700
@@ -32,7 +32,7 @@
 
 \begin{proof}
 (Sketch)
-This is a standard result; see, for example, \nn{need citations}.
+This is a standard result; see, for example, \nn{need citations: Spanier}.
 
 We will build a chain map $f\in \Compat(D^\bullet_*)$ inductively.
 Choose $f(x_{0j})\in D^{0j}_0$ for all $j$

--- a/text/blobdef.tex	Tue Sep 21 07:37:41 2010 -0700
+++ b/text/blobdef.tex	Tue Sep 21 14:44:17 2010 -0700
@@ -67,13 +67,11 @@
 just erasing the blob from the picture
 (but keeping the blob label $u$).
 
-\nn{it seems rather strange to make this a theorem} 
-\nn{it's a theorem because it's stated in the introduction, and I wanted everything there to have numbers that pointed into the paper --S}
 Note that directly from the definition we have
-\begin{thm}
+\begin{prop}
 \label{thm:skein-modules}
 The skein module $A(X)$ is naturally isomorphic to $\bc_0(X)/\bd(\bc_1(X))) = H_0(\bc_*(X))$.
-\end{thm}
+\end{prop}
 This also establishes the second 
 half of Property \ref{property:contractibility}.
 
@@ -292,7 +290,6 @@
 and $s:C \to \cF(B_i)$ is some fixed section of $e$.)
 
 For lack of a better name, 
-\nn{can we think of a better name?}
 we'll call elements of $P$ cone-product polyhedra, 
 and say that blob diagrams have the structure of a cone-product set (analogous to simplicial set).
 \end{remark}

--- a/text/comm_alg.tex	Tue Sep 21 07:37:41 2010 -0700
+++ b/text/comm_alg.tex	Tue Sep 21 14:44:17 2010 -0700
@@ -135,7 +135,7 @@
 0, $\z/j \z$ in odd degrees, and 0 in positive even degrees.
 The point $\Sigma^0(S^1)$ contributes the homology of $BS^1$ which is $\z$ in even 
 degrees and 0 in odd degrees.
-This agrees with the calculation in \cite[3.1.7]{MR1600246}.
+This agrees with the calculation in \cite[\S 3.1.7]{MR1600246}.
 
 \medskip
 
@@ -189,7 +189,5 @@
 \begin{itemize}
 \item compare the topological computation for truncated polynomial algebra with \cite{MR1600246}
 \item multivariable truncated polynomial algebras (at least mention them)
-\item ideally, say something more about higher hochschild homology (maybe sketch idea for proof of equivalence)
-\item say something about SMCs as $n$-categories, e.g. Vect and K-theory.
 \end{itemize}
 

--- a/text/evmap.tex	Tue Sep 21 07:37:41 2010 -0700
+++ b/text/evmap.tex	Tue Sep 21 14:44:17 2010 -0700
@@ -191,7 +191,7 @@
 and with $\supp(x_k) = U$.
 We can now take $d_j \deq \sum x_k$.
 It is clear that $\bd d_j = \sum (g_{j-1}(e_k) - g_j(e_k)) = g_{j-1}(s(\bd b)) - g_{j}(s(\bd b))$, as desired.
-\nn{should maybe have figure}
+\nn{should have figure}
 
 We now define 
 \[
@@ -210,8 +210,6 @@
 For sufficiently fine $\cV_{l-1}$ this will be possible.
 Since $C_*$ is finite, the process terminates after finitely many, say $r$, steps.
 We take $\cV_r = \cU$.
-
-\nn{should probably be more specific at the end}
 \end{proof}
 
 
@@ -222,8 +220,6 @@
 We give $\BD_k$ the finest topology such that
 \begin{itemize}
 \item For any $b\in \BD_k$ the action map $\Homeo(X) \to \BD_k$, $f \mapsto f(b)$ is continuous.
-\item \nn{don't we need something for collaring maps?}
-\nn{KW: no, I don't think so.  not unless we wanted some extension of $CH_*$ to act}
 \item The gluing maps $\BD_k(M)\to \BD_k(M\sgl)$ are continuous.
 \item For balls $B$, the map $U(B) \to \BD_1(B)$, $u\mapsto (B, u, \emptyset)$, is continuous,
 where $U(B) \sub \bc_0(B)$ inherits its topology from $\bc_0(B)$ and the topology on
@@ -418,7 +414,6 @@
 We also will use the abbreviated notation $CH_*(X) \deq CH_*(X, X)$.
 (For convenience, we will permit the singular cells generating $CH_*(X, Y)$ to be more general
 than simplices --- they can be based on any cone-product polyhedron (see Remark \ref{blobsset-remark}).)
-\nn{this note about our non-standard should probably go earlier in the paper, maybe intro}
 
 \begin{thm}  \label{thm:CH}
 For $n$-manifolds $X$ and $Y$ there is a chain map

--- a/text/intro.tex	Tue Sep 21 07:37:41 2010 -0700
+++ b/text/intro.tex	Tue Sep 21 14:44:17 2010 -0700
@@ -8,7 +8,7 @@
 \begin{itemize}
 \item The 0-th homology $H_0(\bc_*(M; \cC))$ is isomorphic to the usual 
 topological quantum field theory invariant of $M$ associated to $\cC$.
-(See Theorem \ref{thm:skein-modules} later in the introduction and \S \ref{sec:constructing-a-tqft}.)
+(See Proposition \ref{thm:skein-modules} later in the introduction and \S \ref{sec:constructing-a-tqft}.)
 \item When $n=1$ and $\cC$ is just a 1-category (e.g.\ an associative algebra), 
 the blob complex $\bc_*(S^1; \cC)$ is quasi-isomorphic to the Hochschild complex $\HC_*(\cC)$.
 (See Theorem \ref{thm:hochschild} and \S \ref{sec:hochschild}.)
@@ -124,7 +124,7 @@
    } (FU.100);
 \draw[->] (C) -- node[above left=3pt] {restrict to \\ standard balls} (tC);
 \draw[->] (FU.80) -- node[right] {restrict \\ to balls} (C.-80);
-\draw[->] (BC) -- node[right] {$H_0$ \\ c.f. Theorem \ref{thm:skein-modules}} (A);
+\draw[->] (BC) -- node[right] {$H_0$ \\ c.f. Proposition \ref{thm:skein-modules}} (A);
 
 \draw[->] (FU) -- node[left] {blob complex \\ for balls} (Cs);
 \draw[<->] (BC) -- node[right] {$\iso$ by \\ Corollary \ref{cor:new-old}} (BCs);
@@ -286,7 +286,7 @@
 
 The blob complex is a simultaneous generalization of the TQFT skein module construction and of Hochschild homology.
 
-\newtheorem*{thm:skein-modules}{Theorem \ref{thm:skein-modules}}
+\newtheorem*{thm:skein-modules}{Proposition \ref{thm:skein-modules}}
 
 \begin{thm:skein-modules}[Skein modules]
 The $0$-th blob homology of $X$ is the usual 
@@ -308,7 +308,7 @@
 \end{equation*}
 \end{thm:hochschild}
 
-Theorem \ref{thm:skein-modules} is immediate from the definition, and
+Proposition \ref{thm:skein-modules} is immediate from the definition, and
 Theorem \ref{thm:hochschild} is established in \S \ref{sec:hochschild}.
 We also note \S \ref{sec:comm_alg} which describes the blob complex when $\cC$ is a one of 
 certain commutative algebras thought of as $n$-categories.

--- a/text/ncat.tex	Tue Sep 21 07:37:41 2010 -0700
+++ b/text/ncat.tex	Tue Sep 21 14:44:17 2010 -0700
@@ -1034,8 +1034,7 @@
 is more involved.
 We will describe two different (but homotopy equivalent) versions of the homotopy colimit of $\psi_{\cC;W}$.
 The first is the usual one, which works for any indexing category.
-The second construction, we we call the {\it local} homotopy colimit,
-\nn{give it a different name?}
+The second construction, which we call the {\it local} homotopy colimit,
 is more closely related to the blob complex
 construction of \S \ref{sec:blob-definition} and takes advantage of local (gluing) properties
 of the indexing category $\cell(W)$.
@@ -1351,7 +1350,7 @@
 plain ball case.
 Note that a marked pinched product can be decomposed into either
 two marked pinched products or a plain pinched product and a marked pinched product.
-\nn{should give figure}
+\nn{should maybe give figure}
 
 \begin{module-axiom}[Product (identity) morphisms]
 For each pinched product $\pi:E\to M$, with $M$ a marked $k$-ball and $E$ a marked
@@ -1828,7 +1827,7 @@
 where $B^j$ is the standard $j$-ball.
 A 1-marked $k$-ball can be decomposed in various ways into smaller balls, which are either 
 (a) smaller 1-marked $k$-balls, (b) 0-marked $k$-balls, or (c) plain $k$-balls.
-(See Figure \nn{need figure}.)
+(See Figure \nn{need figure, and improve caption on other figure}.)
 We now proceed as in the above module definitions.
 
 \begin{figure}[t] \centering
@@ -2190,7 +2189,7 @@
 
 \begin{lem}
 Assume $n\ge 2$ and fix $E$ and $E'$ as above.
-The any two sequences of elementary moves connecting $E$ to $E'$
+Then any two sequences of elementary moves connecting $E$ to $E'$
 are related by a sequence of the two movie moves defined above.
 \end{lem}
 
@@ -2211,7 +2210,7 @@
 rotating the 0-sphere $E$ around the 1-sphere $\bd X$.
 But if $n=1$, then we are in the case of ordinary algebroids and bimodules,
 and this is just the well-known ``Frobenius reciprocity" result for bimodules.
-\nn{find citation for this.  Evans and Kawahigashi?}
+\nn{find citation for this.  Evans and Kawahigashi? Bisch!}
 
 \medskip
 
@@ -2240,7 +2239,7 @@
 
 \medskip
 
-\nn{Stuff that remains to be done (either below or in an appendix or in a separate section or in
-a separate paper): discuss Morita equivalence; functors}
+%\nn{Stuff that remains to be done (either below or in an appendix or in a separate section or in
+%a separate paper): discuss Morita equivalence; functors}