There is a unique real tight contact 3-ball

TL;DR

This paper proves the uniqueness of the real tight contact structure on the 3-ball with convex boundary and provides a partial classification of certain real tight solid tori, advancing the understanding of real contact topology.

Contribution

It establishes the uniqueness of the real tight contact structure on the 3-ball and classifies specific real tight solid tori using real contact neighborhood theorems.

Findings

Uniqueness of real tight contact structure on the 3-ball with convex boundary.

Partial classification of real tight solid tori with antipodal and identity real structures.

Application of real contact neighborhood theorems and invariant convex surface theory.

Abstract

We prove that there is a unique real tight contact structure on the 3-ball with convex boundary up to isotopy through real tight contact structures. We also give a partial classification of the real tight solid tori with the real structure being antipodal map along longitudinal and the identity along meridional direction. For the proofs, we use the real versions of contact neighborhood theorems and the invariant convex surface theory in real contact manifolds.