Floer theory in spaces of stable pairs over Riemann surfaces

Floer theory in spaces of stable pairs over Riemann surfaces

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Tim Perutz , University of Texas, Austin and IAS
IAS Room S-101

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.