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

Abstract

In Contact 3-manifolds, twenty years since J. Martinet’s work, Eliashberg proved that two overtwisted contact structures on a closed oriented 3-manifold are isotopic through contact structures 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.