--- a/blob to-do Sat May 07 09:18:37 2011 -0700
+++ b/blob to-do Sat May 07 09:27:21 2011 -0700
@@ -15,7 +15,7 @@
* Consider moving A_\infty stuff to a subsection
-* dimension n+1, explain the statement and refer to KW's notes
+* (?) dimension n+1, explain the statement and refer to KW's notes. [this was PT's suggestion, but it's sort of already in there. do we need to do more?]
* framings and duality -- work out what's going on!
--- a/text/tqftreview.tex Sat May 07 09:18:37 2011 -0700
+++ b/text/tqftreview.tex Sat May 07 09:27:21 2011 -0700
@@ -437,13 +437,14 @@
a $k$-category $A(Y)$ to an $n{-}k$-manifold $Y$, for $0 \le k \le n$.
These invariants fit together via actions and gluing formulas.
We describe only the case $k=1$ below.
+
The construction of the $n{+}1$-dimensional part of the theory (the path integral)
requires that the starting data (fields and local relations) satisfy additional
conditions.
We do not assume these conditions here, so when we say ``TQFT" we mean a decapitated TQFT
that lacks its $n{+}1$-dimensional part.
Such a ``decapitated'' TQFT is sometimes also called an $n+\epsilon$ or
-$n+\frac{1}{2}$ dimensional TQFT, referring to the fact that it assigns maps to
+$n+\frac{1}{2}$ dimensional TQFT, referring to the fact that it assigns maps to $n{+}1$-dimensional
mapping cylinders between $n$-manifolds, but nothing to arbitrary $n{+}1$-manifolds.
Let $Y$ be an $n{-}1$-manifold.