--- a/text/tqftreview.tex	Wed Jun 29 23:06:29 2011 -0700
+++ b/text/tqftreview.tex	Mon Jul 04 10:25:42 2011 -0600
@@ -192,6 +192,14 @@
 the gluing map is surjective.
 We say that fields in the image of the gluing map
 are transverse to $Y$ or splittable along $Y$.
+\item Splittings.
+Let $c\in \cC_k(X)$ and let $Y\sub X$ be a codimension 1 properly embedded submanifold of $X$.
+Then for most small perturbations of $Y$ (i.e.\ for an open dense
+subset of such perturbations) $c$ splits along $Y$.
+(In Example \ref{ex:maps-to-a-space(fields)}, $c$ splits along all such $Y$.
+In Example \ref{ex:traditional-n-categories(fields)}, $c$ splits along $Y$ so long as $Y$ 
+is in general position with respect to the cell decomposition
+associated to $c$.)
 \item Product fields.
 There are maps $\cC_{k-1}(Y) \to \cC_k(Y \times I)$, denoted
 $c \mapsto c\times I$.