Continuation homomorphism in Rabinowitz Floer homology for symplectic deformations

TL;DR

This paper presents an alternative proof for Rabinowitz Floer homology computations above Mane's critical value by constructing a continuation homomorphism for symplectic deformations, simplifying the process using an isoperimetric inequality.

Contribution

It introduces a new continuation homomorphism for symplectic deformations, enabling reduction to the untwisted case in Rabinowitz Floer homology calculations.

Findings

Constructed a continuation homomorphism for symplectic deformations.

Reduced the computation to the untwisted case.

Utilized a special isoperimetric inequality above Mane's critical value.

Abstract

Will Merry computed Rabinowitz Floer homology above Mane's critical value in terms of loop space homology by establishing an Abbondandolo-Schwarz short exact sequence. The purpose of this article 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 Mane's critical value holds true.