Geometric criteria for overtwistedness

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.

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

Cited by in corpus (4)

• Braided embeddings of contact 3-manifolds in the standard contact 5-sphere
• Simplifying Weinstein Morse functions
• Existence and classification of overtwisted contact structures in all dimensions
• On positive loops of loose Legendrian embeddings