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

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.Comment: Reference updated, The proof of Lemma 3.1 is modified with more detail