Contact manifolds and Weinstein h-cobordisms

TL;DR

This paper demonstrates that high-dimensional contact manifolds connected by certain Weinstein h-cobordisms become contactomorphic after stabilization, and provides examples of non-conjugate contact structures with symplectomorphic symplectizations.

Contribution

It establishes a stabilization result for contact manifolds related by flexible Weinstein h-cobordisms and presents examples of non-conjugate structures with identical symplectizations.

Findings

Contact manifolds become contactomorphic after stabilization

Existence of non-conjugate contact structures with symplectomorphic symplectizations

Extension of h-cobordism techniques to contact topology

Abstract

We prove that closed connected contact manifolds of dimension $\geq 5$ related by an h-cobordism with a flexible Weinstein structure become contactomorphic after some kind of stabilization. We also provide examples of non-conjugate contact structures on a closed manifold with exact symplectomorphic symplectizations.