Continuation homomorphism in Rabinowitz Floer homology for symplectic deformations

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.

29 pages, 1 figure

References in corpus (7)

• Functors and Computations in Floer homology with Applications Part II
• Growth of maps, distortion in groups and symplectic geometry
• Symplectic topology of Mañé's critical values
• Deformations of symplectic cohomology and exact Lagrangians in ALE spaces
• The Arnold-Givental conjecture and moment Floer homology
• Spectral Invariants in Rabinowitz Floer homology and Global Hamiltonian perturbations
• Index computations in Rabinowitz Floer homology

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• Periodic orbits in virtually contact structures
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• On the Rabinowitz Floer homology of twisted cotangent bundles
• An overtwisted disk in a virtual contact structure and the Weinstein conjecture
• On magnetic leaf-wise intersections