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.
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