Gromov's alternative, contact shape, and C^0-rigidity of contact diffeomorphisms

Abstract

We prove that the group of contact diffeomorphisms is closed in the group of all diffeomorphisms in the C^0-topology. By Gromov's alternative, it suffices to exhibit a diffeomorphism that can not be approximated uniformly by contact diffeomorphisms. Our construction uses Eliashberg's contact shape.

9 pages

References in corpus (2)

• Geometry of contact transformations and domains: orderability versus squeezing
• Topological contact dynamics II: topological automorphisms, contact homeomorphisms, and non-smooth contact dynamical systems