Princeton Symplectic Geometry Seminar

Abstract: We revisit Fintushel and Stern's ``rim surgery'' construction from the point of view of Heegaard Floer theory. Our main result is that given a symplectic surface S with simply-connected complement in a symplectic 4-manifold, there exist infinitely many smoothly non-isotopic surfaces representing the topological isotopy class of S, so long as the self-intersection of the surface in question is not ``too negative.'' This extends the result of Fintushel and Stern, who were obliged to assume that the self-intersection was at least 0. The proof makes use of a result giving the behavior of relative Ozsvath-Szabo invariants under Fintushel-Stern knot surgery, together with a calculation of the twisted Floer homology of circle bundles with ``large'' Euler number over surfaces. We will give an outline of the proof, in particular attempt to indicate why the restriction on the self-intersection of S arises.