Functoriality in surgery theory: geometric remarks and implications

Shmuel Weinberger
Friday, July 26, 2013 - from 11:00 to 12:00
It is a remarkable fact that the surgery theoretic classification of manifolds - in the topological setting - has some functoriality properties: One can push forward a manifold homotopy equivalent to M to one homotopy equivalent to N under a continuous map from M to N, under appropriate dimension and orientation conditions. We shall discuss this and equivariant and stratified variants, and show how things like the existence of nonresolvable homology manifolds, counterexamples to the equivariant Borel conjecture, embedding theorems and calculations of certain types of equivariant structure sets follow quite painlessly from such statements. I will also attempt to give some indication of the sources of these functorialities. (Much of this talk will be based on joint work with Sylvain Cappell and Min Yan.)