Abstract
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.
Original language | English (US) |
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Pages (from-to) | 563-604 |
Number of pages | 42 |
Journal | Journal of the American Mathematical Society |
Volume | 32 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2019 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics