Hamiltonian Floer homology for compact convex symplectic manifolds

TL;DR

This paper develops Hamiltonian Floer homology theories for compact convex symplectic manifolds with boundary, establishing isomorphisms with quantum homology and defining spectral invariants.

Contribution

It constructs absolute and relative Floer homology algebras with ring structures and proves isomorphisms to quantum homology for convex symplectic manifolds.

Findings

Construction of Floer homology algebras for convex symplectic manifolds.

Establishment of Piunikhin-Salamon-Schwarz isomorphisms.

Definition of spectral invariants for Hamiltonian diffeomorphisms.

Abstract

We construct absolute and relative versions of Hamiltonian Floer homology algebras for strongly semi-positive compact symplectic manifolds with convex boundary, where the ring structures are given by the appropriate versions of the pair-of-pants products. We establish the absolute and relative Piunikhin-Salamon-Schwarz isomorphisms between these Floer homology algebras and the corresponding absolute and relative quantum homology algebras. As a result, the absolute and relative analogues of the spectral invariants on the group of compactly supported Hamiltonian diffeomorphisms are defined.