Heegaard Floer symplectic cohomology and generalized Viterbo’s isomorphism theorem

Abstract: In recent years several groups of authors introduced various invariants that are based on Lagrangian Floer homology of a symmetric product of a symplectic manifold. In this talk, I will introduce Heegaard Floer symplectic cohomology (HFSH), an invariant of a Liouville domain M which mimics symplectic cohomology of the k-th symmetric product of M. This invariant can also be regarded as a deformation of the k-th symmetric version of symplectic cohomology, obtained by counting curves of higher genus. I will also introduce a multiloop Morse complex and show that for cotangent bundles this complex computes HFSH. This is a joint work with Tianyu Yuan.