--- a/text/basic_properties.tex	Fri Jul 30 18:36:08 2010 -0400
+++ b/text/basic_properties.tex	Fri Jul 30 20:19:17 2010 -0400
@@ -86,8 +86,8 @@
 Note that $S$ is a disjoint union of balls.
 Assign to $b$ the acyclic (in positive degrees) subcomplex $T(b) \deq r\bullet\bc_*(S)$.
 Note that if a diagram $b'$ is part of $\bd b$ then $T(B') \sub T(b)$.
-Both $f$ and the identity are compatible with $T$ (in the sense of acyclic models), 
-so $f$ and the identity map are homotopic. \nn{We should actually have a section \S \ref{sec:moam} with a definition of ``compatible" and this statement as a lemma}
+Both $f$ and the identity are compatible with $T$ (in the sense of acyclic models, \S\ref{sec:moam}), 
+so $f$ and the identity map are homotopic.
 \end{proof}
 
 For the next proposition we will temporarily restore $n$-manifold boundary

--- a/text/blobdef.tex	Fri Jul 30 18:36:08 2010 -0400
+++ b/text/blobdef.tex	Fri Jul 30 20:19:17 2010 -0400
@@ -177,9 +177,20 @@
 In the example above, note that $$A \sqcup B \sqcup C \sqcup D \to (A \cup B) \sqcup (C \cup D) \to A \cup B \cup C \cup D$$ is a  ball decomposition, but other sequences of gluings starting from $A \sqcup B \sqcup C \sqcup D$have intermediate steps which are not manifolds.
 
 We'll now slightly restrict the possible configurations of blobs.
+%%%%% oops -- I missed the similar discussion after the definition
+%The basic idea is that each blob in a configuration 
+%is the image a ball, with embedded interior and possibly glued-up boundary;
+%distinct blobs should either have disjoint interiors or be nested;
+%and the entire configuration should be compatible with some gluing decomposition of $X$.
 \begin{defn}
 \label{defn:configuration}
-A configuration of $k$ blobs in $X$ is an ordered collection of $k$ subsets $\{B_1, \ldots B_k\}$ of $X$ such that there exists a gluing decomposition $M_0  \to \cdots \to M_m = X$ of $X$ and for each subset $B_i$ there is some $0 \leq r \leq m$ and some connected component $M_r'$ of $M_r$ which is a ball, so $B_i$ is the image of $M_r'$ in $X$. Such a gluing decomposition is \emph{compatible} with the configuration. A blob $B_i$ is a twig blob if no other blob $B_j$ maps into the appropriate $M_r'$. \nn{that's a really clumsy way to say it, but I struggled to say it nicely and still allow boundaries to intersect -S}
+A configuration of $k$ blobs in $X$ is an ordered collection of $k$ subsets $\{B_1, \ldots B_k\}$ 
+of $X$ such that there exists a gluing decomposition $M_0  \to \cdots \to M_m = X$ of $X$ and 
+for each subset $B_i$ there is some $0 \leq r \leq m$ and some connected component $M_r'$ of 
+$M_r$ which is a ball, so $B_i$ is the image of $M_r'$ in $X$. 
+We say that such a gluing decomposition 
+is \emph{compatible} with the configuration. 
+A blob $B_i$ is a twig blob if no other blob $B_j$ is a strict subset of it. 
 \end{defn}
 In particular, this implies what we said about blobs above: 
 that for any two blobs in a configuration of blobs in $X$, 

--- a/text/ncat.tex	Fri Jul 30 18:36:08 2010 -0400
+++ b/text/ncat.tex	Fri Jul 30 20:19:17 2010 -0400
@@ -871,7 +871,6 @@
 \begin{example}[$E_n$ algebras]
 \rm
 \label{ex:e-n-alg}
-
 Let $A$ be an $\cE\cB_n$-algebra.
 Note that this implies a $\Diff(B^n)$ action on $A$, 
 since $\cE\cB_n$ contains a copy of $\Diff(B^n)$.
@@ -892,14 +891,13 @@
 also comes from the $\cE\cB_n$ action on $A$.
 \nn{should we spell this out?}
 
-\nn{Should remark that the associated hocolim for manifolds
-agrees with Lurie's topological chiral homology construction; maybe wait
-until next subsection to say that?}
-
 Conversely, one can show that a topological $A_\infty$ $n$-category $\cC$, where the $k$-morphisms
 $\cC(X)$ are trivial (single point) for $k<n$, gives rise to 
 an $\cE\cB_n$-algebra.
 \nn{The paper is already long; is it worth giving details here?}
+
+If we apply the homotopy colimit construction of the next subsection to this example, 
+we get an instance of Lurie's topological chiral homology construction.
 \end{example}
 
 
@@ -2355,20 +2353,17 @@
 In particular, if $F: X\to X$ is the identity on $\bd X$ then $f$ acts trivially, as required by
 Axiom \ref{axiom:extended-isotopies} of \S\ref{ss:n-cat-def}.
 
-
-\nn{still to do: gluing, associativity, collar maps}
+We define product $n{+}1$-morphisms to be identity maps of modules.
 
-\medskip
-\hrule
-\medskip
-
+To define (binary) composition of $n{+}1$-morphisms, choose the obvious common equator
+then compose the module maps.
 
 
-Stuff that remains to be done (either below or in an appendix or in a separate section or in
-a separate paper):
-\begin{itemize}
-\item discuss Morita equivalence
-\item functors
-\end{itemize}
+\nn{still to do: associativity}
+
+\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}