
diff -r fd6e53389f2c -r 871dffc348ab pnas/pnas.tex
--- a/pnas/pnas.tex	Sun Nov 14 15:39:03 2010 -0800
+++ b/pnas/pnas.tex	Sun Nov 14 15:45:26 2010 -0800
@@ -462,7 +462,13 @@
 Boundary restrictions and gluing are again straightforward to define.
 Define product morphisms via product cell decompositions.
 
+\subsection{Example (bordism)}
+When $X$ is a $k$-ball with $k<n$, $\Bord^n(X)$ is the set of all $k$-dimensional
+submanifolds $W$ in $X\times \bbR^\infty$ which project to $X$ transversely
+to $\bd X$.
+For an $n$-ball $X$ define $\Bord^n(X)$ to be homeomorphism classes rel boundary of such $n$-dimensional submanifolds.
 
+There is an $A_\infty$ analogue enriched in topological spaces, where at the top level we take all such submanifolds, rather than homeomorphism classes. For each fixed $\bdy W \subset \bdy X \times \bbR^\infty$, we can topologize the set of submanifolds by ambient isotopy rel boundary.
 
 \subsection{The blob complex}
 \subsubsection{Decompositions of manifolds}




