GT seminar: Fixed point Floer cohomology of Dehn twists

Abstract: Fixed point Floer cohomology is a Floer theoretic invariant associated to symplectomorphisms of a symplectic manifold. It has a “product” structure which we can assemble into a ring. In previous joint work Maxim Jeffs and Ziwen Zhao we fully computed this ring for Dehn twists on surfaces, and the results verified predictions from mirror symmetry. Furthermore, we constructed a “quantum cohomology” for singular symplectic surfaces using this ring that also matched expectations from mirror symmetry. I will survey this body of work and discuss some work in preparation towards computing this ring structure in higher dimensional Dehn twists - for these computations we shall see some interplay between string topology and morse homology.

This is a talk in our Geometry and Topology Seminar Series.