A proof of the classification theorem of overtwisted contact structures via convex surface theory

TL;DR

This paper offers an alternative proof of Eliashberg's classification theorem for overtwisted contact structures on closed 3-manifolds, utilizing convex surface theory and bypass techniques.

Contribution

It introduces a new proof method for the classification theorem, simplifying the understanding of overtwisted contact structures.

Findings

Alternative proof of Eliashberg's theorem

Use of convex surface theory and bypasses

Simplified approach to classifying overtwisted contact structures

Abstract

In 1989, Y. Eliashberg proved that two overtwisted contact structures on a closed oriented 3-manifold are isotopic if and only if they are homotopic as 2-plane fields. We provide an alternative proof of this theorem using the convex surface theory and bypasses.