Geometry & Topology Seminar: "Stable equivalence of smoothly knotted surfaces"

Abstract:  It is well known that there are smoothly inequivalent, objects in 4-dimensions that are topologically equivalent. Fairly general results exist stating that such objects become smoothly equivalent after some number of stabilizations. Until this past summer the only thing known about the number of stabilizations needed was an infinite collection of examples where one stabilization was enough.

This talk will present the proof of a theorem demonstrating that when the easiest topological invariants are trivial two smooth surfaces become smoothly isotopic after just one stabilization. 
This is joint work with Kim, Melvin, Ruberman and Schwartz.

We will also present joint work with Ruberman aimed at the difference between the homotopy groups of the diffeomorphism group and the homotopy groups of the homeomorphism group.

Host: Rachel Roberts