skip to main content

Geometry and Topology Seminar

Friday, February 2, 2024
4:00pm to 5:00pm
Add to Cal
Linde Hall 187
Heegaard Floer symplectic cohomology and generalized Viterbo's isomorphism
Roman Krutowski, Department of Mathematics, UCLA,

I will define a novel invariant, called Heegaard Floer symplectic cohomology (HFSH), which serves as a closed string analog of the higher-dimensional Heegaard Floer homology. This invariant can also be regarded as a deformation of a k-th symmetric version of symplectic cohomology given by counting curves of higher genus. Alternatively, one may view it as a Floer invariant associated with a problem of Hamiltonian motion of multiple identical particles.  I will also introduce a multiloop Morse complex of a manifold, which is supposed to be a Morse-theoretic counterpart of HFSH. At last, I will show that HFSH of a cotangent bundle T^*M is isomorphic to the cohomology of the multiloop complex of M. This result generalizes Viterbo's isomorphism theorem to the case of multiple particles.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit