On the violation of Thurston-Bennequin inequality for a certain non-convex hypersurface

TL;DR

This paper demonstrates that in higher-dimensional contact manifolds, there exist non-convex hypersurfaces that violate the Thurston-Bennequin inequality, challenging previous assumptions about convexity constraints.

Contribution

It constructs explicit examples of non-convex hypersurfaces violating the Thurston-Bennequin inequality in contact manifolds of dimension greater than three.

Findings

Existence of non-convex hypersurfaces violating the inequality

Violation occurs in any open subset of the manifold

Challenges convexity assumptions in higher dimensions

Abstract

We show that any open subset of a contact manifold of dimension greater than three contains a certain non-convex hypersurface violating the Thurston-Bennequin inequality.