Rabinowitz Floer homology of negative line bundles and Floer Gysin sequence

TL;DR

This paper develops a refined Rabinowitz Floer homology for negative line bundles, introduces a Floer Gysin sequence, and applies these tools to problems in symplectic topology and prequantization spaces.

Contribution

It constructs a new version of Rabinowitz Floer homology, establishes a Gysin-type long exact sequence, and provides computational results and applications.

Findings

Established a Gysin-type long exact sequence for the new invariant

Constructed a short exact sequence for ordinary Rabinowitz Floer homology

Applied the theory to the orderability problem in prequantization spaces

Abstract

This article is concerned with the Rabinowitz Floer homology of negative line bundles. We construct a refined version of Rabinowitz Floer homology and study its properties. In particular, we build a Gysin-type long exact sequence for this new invariant and discuss an application to the orderability problem for prequantization spaces. We also construct a short exact sequence for the ordinary Rabinowitz Floer homology and provide computational results.