10/23/2003

Peter Ozsvath
Columbia University and IAS

I will discuss joint work with Peter Kronheimer, Tom Mrowka, and Zoltan Szabo, in which we use methods from gauge theory to verify a conjecture of Gordon, according to which if p/q Dehn surgery on a knot K is orientation preservingly diffeomorphic to p/q Dehn surgery along the unknot U, then K=U. The key technical device is a surgery long exact sequence for Seiberg-Witten monopole Floer homology. There are other applications of these techniques to problems of lens space surgeries, and also to the non-existence of taut foliations over certain three-manifolds.