$C^0$ contact geometry of isotropic submanifolds

Abstract: The celebrated Eliashberg-Gromov rigidity theorem states that a diffeomorphism which is a $C^0$-limit of symplectomorphisms is itself symplectic. Contact version of this rigidity theorem holds true as well. Motivated by this, contact homeomorphisms are defined as $C^0$-limits of contactomorphisms. Isotropic submanifolds are a particularly interesting class of submanifolds, and in this talk we will try to answer whether or not isotropic property is preserved by contact homeomorphisms. Legendrian submanifolds are isotropic submanifolds of maximal dimension and we expect that the rigidity holds in this case. We give a new proof of the rigidity in dimension 3, and provide some type of rigidity in higher dimensions. On the other hand, we show that the subcritical isotropic curves are flexible, and we prove quantitative $h$-principle for subcritical isotropic embeddings which is our main tool for proving the flexibility result.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

Series comments: On the week of the seminar, an announcement with the Zoom link is mailed to the seminar mailing list. To receive these e-mails, please sign up by writing to Lev Buhovsky (http://www.math.tau.ac.il/~levbuh/).