diff -r 032d3c2b2a89 -r 249ccaa26fee text/tqftreview.tex --- 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.