Spectral Invariants in Rabinowitz Floer homology and Global Hamiltonian perturbations

TL;DR

This paper extends spectral invariants from Hamiltonian Floer homology to Rabinowitz Floer homology, enabling new quantitative results on leaf-wise intersections even in degenerate cases.

Contribution

It introduces spectral invariants in Rabinowitz Floer homology and applies them to derive existence results for leaf-wise intersections in degenerate settings.

Findings

Spectral invariants are successfully extended to Rabinowitz Floer homology.

New quantitative existence results for leaf-wise intersections are established.

Critical points are shown to exist even when the Rabinowitz action functional is degenerate.

Abstract

Spectral invariant were introduced in Hamiltonian Floer homology by Viterbo, Oh, and Schwarz. We extend this concept to Rabinowitz Floer homology. As an application we derive new quantitative existence results for leaf-wise intersections. The importance of spectral invariants for the presented application is that spectral invariants allow us to derive existence of critical points of the Rabinowitz action functional even in degenerate situations where the functional is not Morse.