Geometric criteria for overtwistedness

By Roger Casals, Emmy Murphy, F. Presas. Journal of The American Mathematical Society, 2015

57 citations recorded by the source corpus.

In this article we establish efficient geometric criteria to decide whether a contact manifold is overtwisted. Starting with the original definition, we first relate overtwisted disks in different dimensions and show that a manifold is overtwisted if and only if the Legendrian unknot admits a loose chart. Then we characterize overtwistedness in terms of the monodromy of open book decompositions and contact surgeries. Finally, we provide several applications of these geometric criteria.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/71bb11eb73ccae74e6ed25a3f233e7b888d9d0bb

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In Geometry and Topology

1. Roger Casals
2. Emmy Murphy

In Mathematical Physics

1. Roger Casals
2. Emmy Murphy

Citations in the corpus

• Legendrian fronts for affine varieties (2016, background): “particular, a given Legendrian might not be loose in a contact manifold ( Y;˘) and become loose if we modify the contact structure (Y;˘) in a Darboux chart disjoint from an open neighborhood of , see [17, 18, 56]. Loose Legendrian submanifolds have been classied up to Legendrian isotopy in the artic”