English

Geometric criteria for overtwistedness

Symplectic Geometry 2018-11-22 v2

Abstract

We establish geometric criteria to decide whether a contact manifold is overtwisted. Starting with the original definition, we first relate the different overtwisted disks in each dimension and show that a manifold is overtwisted if the Legendrian unknot is loose. Then we characterize overtwistedness in terms of open book decompositions and provide several applications.

Keywords

Cite

@article{arxiv.1503.06221,
  title  = {Geometric criteria for overtwistedness},
  author = {Roger Casals and Emmy Murphy and Francisco Presas},
  journal= {arXiv preprint arXiv:1503.06221},
  year   = {2018}
}

Comments

37 Pages. Significantly revised version. In particular, more details added in the Proof of Theorem 3.2. This version to appear in J. Amer. Math. Soc

R2 v1 2026-06-22T08:58:26.900Z