Floer homology for negative line bundles and Reeb chords in pre-quantization spaces

TL;DR

This paper establishes the existence of Reeb orbits for Bohr-Sommerfeld Legendrians in pre-quantization spaces by analyzing Floer homology on negative line bundles, providing quantitative lower bounds.

Contribution

It introduces a Floer homology approach for negative line bundles to prove Reeb orbit existence and offers explicit quantitative estimates.

Findings

Reeb orbits exist for certain Legendrians in pre-quantization spaces.

Quantitative lower bounds for Reeb orbit action are derived.

Floer homology on negative line bundles is effective for studying Reeb dynamics.

Abstract

In this article we prove existence of Reeb orbits for Bohr-Sommerfeld Legendrians in certain pre-quantization spaces. We give a quantitative estimate from below. These estimates are obtained by studying Floer homology for fibre-wise quadratic Hamiltonian functions on negative line bundles.