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arXiv · 1503.06221

Geometric criteria for overtwistedness

Roger Casals·Emmy Murphy·Francisco Presas
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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.

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Roger Casals, Emmy Murphy, Francisco Presas. 2015-03-20. Geometric criteria for overtwistedness. https://arxiv.org/abs/1503.06221

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