Floer theory in spaces of stable pairs over Riemann surfaces

Princeton/IAS Symplectic Geometry Seminar
Topic:Floer theory in spaces of stable pairs over Riemann surfaces
Speaker:Timothy Perutz
Affiliation:University of Texas, Austin; von Neumann Fellow, School of Mathematics
Date:Thursday, May 4
Time/Room:10:45am - 11:45am/S-101
Video Link:https://video.ias.edu/puias/2017/0504-TimothyPerutz

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” analog 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.