Floer theory in spaces of stable pairs over Riemann surfaces
Floer theory in spaces of stable pairs over Riemann surfaces

Tim Perutz , University of Texas, Austin and IAS
IAS Room S101
I will report on joint work with Andrew Lee, which explores the notion that spaces of stable pairs over Riemann surfaces (in the sense of Bradlow and Thaddeus) could form a natural home for a "nonabelian" analog of Heegaard Floer homology for 3manifolds  just as the gfold symmetric product is the home of Heegaard Floer homology  thereby circumventing the problems with singularities that beset instantontype theories. In an initial foray into this area, we set up a theory not for Heegaard splittings but for fibered 3manifolds, based on fixedpoint Floer homology. We show that, when the fiber has genus 1, it contains the expected information from the SeibergWitten Floer theory of the fibered 3manifold.