Hamiltonian Floer homology for compact convex symplectic manifolds

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.

29 pages. The final version appeared in Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. Version 3 is the last arxiv version: various corrections and clarifications were made, references were added

References in corpus (2)

• Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds
• Quantum homology of compact convex symplectic manifolds

Cited by in corpus (3)

• Quasi-morphisms on contactomorphism groups and contact rigidity
• The sharp energy-capacity inequality on convex symplectic manifolds
• Product and Coproduct on Fixed Point Floer Homology of Positive Dehn Twists