Contact manifolds with symplectomorphic symplectizations

TL;DR

This paper constructs examples of higher-dimensional contact manifolds that are topologically distinct but share identical symplectizations, highlighting subtle differences in contact topology.

Contribution

It introduces new examples of contact manifolds with symplectomorphic symplectizations that are not diffeomorphic, expanding understanding of contact and symplectic geometry.

Findings

Existence of non-diffeomorphic contact manifolds with identical symplectizations

Examples in all odd dimensions ≥ 5

Insights into the relationship between contact topology and symplectic geometry

Abstract

We provide examples of contact manifolds of any odd dimension $\geq 5$ which are not diffeomorphic but have exact symplectomorphic symplectizations.