
diff -r c06a899bd1f0 -r d3b05641e7ca text/intro.tex
--- a/text/intro.tex	Sun Jul 04 13:15:03 2010 -0600
+++ b/text/intro.tex	Sun Jul 04 23:32:48 2010 -0600
@@ -38,7 +38,7 @@
 and establishes some of its properties.
 There are many alternative definitions of $n$-categories, and part of our difficulty defining the blob complex is 
 simply explaining what we mean by an ``$n$-category with strong duality'' as one of the inputs.
-At first we entirely avoid this problem by introducing the notion of a `system of fields', and define the blob complex 
+At first we entirely avoid this problem by introducing the notion of a ``system of fields", and define the blob complex 
 associated to an $n$-manifold and an $n$-dimensional system of fields.
 We sketch the construction of a system of fields from a $1$-category or from a pivotal $2$-category.
 
@@ -50,7 +50,7 @@
 We call these ``topological $n$-categories'', to differentiate them from previous versions.
 Moreover, we find that we need analogous $A_\infty$ $n$-categories, and we define these as well following very similar axioms.
 
-The basic idea is that each potential definition of an $n$-category makes a choice about the `shape' of morphisms.
+The basic idea is that each potential definition of an $n$-category makes a choice about the ``shape" of morphisms.
 We try to be as lax as possible: a topological $n$-category associates a vector space to every $B$ homeomorphic to the $n$-ball.
 These vector spaces glue together associatively, and we require that there is an action of the homeomorphism groupoid.
 For an $A_\infty$ $n$-category, we associate a chain complex instead of a vector space to each such $B$ and ask that the action of 
@@ -61,10 +61,10 @@
 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 
 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 
+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.
 We use the blob complex for $A_\infty$ $n$-categories to establish important properties of the blob complex (in both variants), 
-in particular the `gluing formula' of Theorem \ref{thm:gluing} below.
+in particular the ``gluing formula" of Theorem \ref{thm:gluing} below.
 
 The relationship between all these ideas is sketched in Figure \ref{fig:outline}.
 
@@ -115,7 +115,7 @@
 thought of as a topological $n$-category, in terms of the topology of $M$.
 Section \S \ref{sec:deligne} states (and in a later edition of this paper, hopefully proves) 
 a higher dimensional generalization of the Deligne conjecture (that the little discs operad acts on Hochschild cohomology) in terms of the blob complex.
-The appendixes prove technical results about $\CH{M}$ and the `small blob complex', 
+The appendixes prove technical results about $\CH{M}$ and the ``small blob complex", 
 and make connections between our definitions of $n$-categories and familiar definitions for $n=1$ and $n=2$, 
 as well as relating the $n=1$ case of our $A_\infty$ $n$-categories with usual $A_\infty$ algebras.
 
@@ -436,7 +436,7 @@
 The paper ``Skein homology'' \cite{MR1624157} has similar motivations, and it may be 
 interesting to investigate if there is a connection with the material here.
 
-Many results in Hochschild homology can be understood `topologically' via the blob complex.
+Many results in Hochschild homology can be understood ``topologically" via the blob complex.
 For example, we expect that the shuffle product on the Hochschild homology of a commutative algebra $A$ 
 (see \cite[\S 4.2]{MR1600246}) simply corresponds to the gluing operation on $\bc_*(S^1 \times [0,1], A)$, 
 but haven't investigated the details.




