Equivalent notions of high-dimensional overtwistedness

Equivalent notions of high-dimensional overtwistedness

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Emmy Murphy, MIT
Fine Hall 322

In recent joint work with Borman and Eliashberg, a new definition of overtwisted contact structures was given for high-dimensional contact manifolds, which were then classified up to isotopy. However, the definition is fairly cumbersome, so much so that it is essentially impossible to check in any explicit example. This talk will focus on various criteria which are shown to be equivalent to overtwistedness, giving numerous explicit examples of overtwisted contact manifolds, and relating overtwisteness to a number of older works. In particular we show that negatively stabilized open books, looseness of the Legendrian unknot, and existence of a "nice" plastikstufe are all equivalent to overtwistedness. This project is joint work with R. Casals and F. Presas.