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 ‘non-abelian’ analogue of Heegaard Floer homology for 3-manifolds – just as the g-fold symmetric product is the home of Heegaard Floer homology – thereby circumventing the problems with singularities that beset instanton-type theories. In an initial foray into this area, we set up a theory not for Heegaard splittings but for fibered 3-manifolds, based on fixed-point Floer homology. We show that, when the fiber has genus 1, it contains the expected information from the Seiberg-Witten Floer theory of the fibered 3-manifold.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
