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)|
|Number of pages||42|
|Journal||Journal of the American Mathematical Society|
|State||Published - Apr 2019|
All Science Journal Classification (ASJC) codes
- Applied Mathematics