
diff -r c24e59300fca -r 682fd0520c66 text/tqftreview.tex
--- a/text/tqftreview.tex	Tue May 10 14:30:23 2011 -0700
+++ b/text/tqftreview.tex	Wed May 11 14:20:10 2011 -0700
@@ -444,11 +444,13 @@
 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
+(Specifically, $A(X; c)$ is finite dimensional for all $n$-manifolds $X$ and the inner products
+on $A(B^n; c)$ induced by the path integral of $B^{n+1}$ are positive definite for all $c$.)
+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 $n{+}1$-dimensional
-mapping cylinders between $n$-manifolds, but nothing to arbitrary $n{+}1$-manifolds.
+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 linear maps to $n{+}1$-dimensional
+mapping cylinders between $n$-manifolds, but nothing to general $n{+}1$-manifolds.
 
 Let $Y$ be an $n{-}1$-manifold.
 Define a linear 1-category $A(Y)$ as follows.




