Diffeomorphism type via aperiodicity in Reeb dynamics

TL;DR

This paper characterizes the diffeomorphism type of certain contact manifolds using the aperiodicity of Reeb flows, establishing uniqueness under the assumption of no short periodic orbits.

Contribution

It introduces a new method to determine the diffeomorphism type of boundary-shaped neighborhoods via Reeb flow aperiodicity, assuming no short periodic orbits.

Findings

Characterization of boundary-shaped neighborhoods using Reeb flow aperiodicity

Proof of uniqueness of homotopy and diffeomorphism types under certain conditions

Establishment of conditions linking Reeb dynamics to manifold topology

Abstract

We characterise boundary shaped disc like neighbourhoods of certain isotropic submanifolds in terms of aperiodicity of Reeb flows. We prove uniqueness of homotopy and diffeomorphism type of such contact manifolds assuming non-existence of short periodic Reeb orbits.