Geometric criteria for overtwistedness

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...

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Bibliographic Details
Published in:Journal of the American Mathematical Society 2019-04, Vol.32 (2), p.563-604
Main Authors: Casals, Roger, Murphy, Emmy, Presas, Francisco
Format: Article
Language:English
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Summary: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.
ISSN:0894-0347
1088-6834
DOI:10.1090/jams/917