GT seminar: C⁰-Contact Geometry of Surfaces in 3-Manifolds

Abstract: We study the behavior of surfaces in contact 3-manifolds under C⁰-limits of contactomorphisms. We prove that contact homeomorphisms preserve characteristic foliations on surfaces: singular points are mapped to singular points, and the image of every 1-dimensional leaf is again a 1-dimensional leaf in the image surface. As a consequence, regular coisotropic surfaces are C⁰-rigid. In contrast, convex surfaces exhibit C⁰-flexibility: we construct a contact homeomorphism sending a convex 2-torus to a non-convex one. This is joint work with Baptiste Serraille.

This is a talk in our Geometry and Topology Seminar Series.