Concordance surgery and the Ozsvath--Szabo 4-manifold invariant

Ian Zemke
Taplin Auditorium

A major breakthrough in 4-manifold topology was Fintushel and Stern's theorem about knot surgery and the Seiberg-Witten invariant. In this talk, we will discuss a generalization, called concordance surgery, constructed from a self-concordance of a knot in S^3. We prove that the effect on Ozsvath and Szabo's closed 4-manifold invariant is multiplication by a graded Lefschetz number on knot Floer homology. In the process, we will describe some general results about Juhasz's TQFT for sutured Floer homology. This is joint work with Andras Juhasz.