The Large-Scale Geometry of Overtwisted Contact Forms

Abstract: Inspired by the symplectic Banach-Mazur distance, proposed by Ostrover and Polterovich in the setting of non-degenerate starshaped domains of Liouville manifolds, we define a distance on the space of contact forms supporting a given contact structure on a closed contact manifold. We compare it to a recently defined contact Banach-Mazur distance by Rosen and Zhang and we use it in order to bi-Lipschitz embed part of the 2-dimensional Euclidean space into the space of overtwisted contact forms supporting a given contact structure on a smooth closed manifold.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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