Continuation homomorphism in Rabinowitz Floer homology for symplectic deformations

Abstract

Will J. Merry computed Rabinowitz Floer homology above Mañé's critical value in terms of loop space homology in [14] by establishing an Abbondandolo-Schwarz short exact sequence. The purpose of this paper is to provide an alternative proof of Merry's result. We construct a continuation homomorphism for symplectic deformations which enables us to reduce the computation to the untwisted case. Our construction takes advantage of a special version of the isoperimetric inequality which above Mañé's critical value holds true.