Orateur
Michael Usher
Description
The usual filtered Floer homology groups are formal analogues of the homologies of the sublevel sets of a Morse function on a manifold. In the Morse setting,
by instead considering interlevel sets (preimages of general intervals) one obtains an algebraic structure that is classified by a barcode that refines the usual
sublevel persistence barcode. I will describe an algebraic formalism that allows one to adapt this to Floer-theoretic settings. In this case of Hamiltonian Floer
theory this gives rise to a pairing between distinguished spectral invariants of a Hamiltonian flow and of its inverse that satisfies stability and duality theorems.
