The Conley-Zehnder indices of the Reeb flow action along $S^1$-fibers over certain orbifolds

TL;DR

This paper establishes a relation between Conley-Zehnder indices of Reeb flows in prequantization bundles and orbifold Chern classes, extending known results from manifolds to orbifolds, with applications to key examples.

Contribution

It introduces a new relation linking Reeb flow indices and orbifold Chern classes, generalizing from manifolds to orbifolds.

Findings

Derived a formula connecting Conley-Zehnder indices with orbifold Chern classes

Applied the relation to specific examples of orbifolds

Extended known manifold results to orbifold settings

Abstract

We prove a useful relation between the Conley-Zehnder indices of the Reeb vector flow action along periodic orbits in prequantization bundles and the orbifold Chern class of the base symplectic orbifolds motivated by the well-known case of manifolds. We also apply this method to primary examples.