Geometry and Topology Seminar: "Exotic Families of Diffeomorphisms"

Abstract: It is well known that there are distinct smooth four-dimensional manifolds that are homeomorphic. This translates to all facets of topology in four-dimensions. In this lecture we explain how to prove that the kernel of the map from any homotopy group of diffeomorphisms of a four-manifold to the corresponding homotopy group of homeomorphisms is highly non-trivial. We will also describe some variants of this result and perhaps provide some wild speculation to motivate such esoteric questions.

Host: Michael Landry