David Auckly, Kansas State University

Title: Exotic Families of Diffeomorphisms

Abstract: In is now known that the smooth and topological
categories are very different in four dimensions. This is reflected in
the homotopy and homology groups of the diffeomorphism and homeomorphism
group. This talk will describe joint work with Danny Ruberman establishing
that the kernel of the map on any homotopy (or homology group) from the space
of diffeomorphisms to the space of homeomorphisms of certain four manifolds
can be very large.

This requires a construction of a family of diffeomorphisms that
contracts through homeomorphisms, but not through diffeomorphisms. It
requires an invariant to prove that the family cannot smoothly contract,
and a method to compute this invariant. We will address all three points,
construction of families, the definition of an invariant (via counts of
solutions to PDEs) and computation of the invariant.