The equivalence of the Ekeland-Hofer and equivariant symplectic homology capacities

Speaker: Vinicius G. B. Ramos

Date: Thu, Jul 21, 2022

Location: PIMS, University of British Columbia, Zoom, Online

Conference: Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory

Subject: Mathematics

Class: Scientific


The Ekeland-Hofer capacities are some of the earliest symplectic capacities. They were defined without Floer theory and their calculation for ellipsoids and polydisks laid the foundation for the understanding of symplectic embeddings for a long time. More recently, Gutt and Hutchings defined a sequence of capacities using positive S^1 equivariant symplectic homology, which are harder to define, but much easier to compute. In this talk, I will explain how there is an isomorphism from the Hamiltonian Floer homology of a class of Hamiltonians to its H^{1/2}-Morse homology and how this implies that those two sequences of capacities coincide. This is joint work with J. Gutt.