HAMILTONIAN FLOER HOMOLOGY FOR COMPACT CONVEX SYMPLECTIC MANIFOLDS

Abstract. We construct absolute and relative versions of Hamiltonian Floer ho-mology algebras for strongly semi-positive compact symplectic manifolds with con-vex 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. 1. Introduction. In [14] U. Frauenfelder and F. Schlenk defined the Floer homology for weakly exact compact convex symplectic manifolds. The authors also established the Piunikhin– Salamon–Schwarz (PSS) isomorphism between the ring of Floer homology and the ring of Morse homology of such manifolds. This in turn led to the construction o