Gromov's alternative, contact shape, and C⁰-rigidity of contact diffeomorphisms

2013/10/01 by Stefan Müller, Müller, Stefan, Peter Spaeth +2
Biochemistry, Genetics and Molecular Biology · Mathematics · #53D10 #53D35 #57R17 #Cellular Mechanics and Interactions #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #math.SG #msc:53D10 #msc:53D35 #msc:57R17

paper · pdf · doi:10.48550/arxiv.1310.0527

9 pages

openalex publication_date 2013/10/01 · arxiv created 2013/10/02 · arxiv updated 2013/10/03 · openalex created_date 2022/09/15 · openalex updated_date 2026/07/28

Abstract

We prove that the group of contact diffeomorphisms is closed in the group of all diffeomorphisms in the C⁰-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.

Citations

• Topological contact dynamics II: topological automorphisms, contact homeomorphisms, and non-smooth contact dynamical systems

Related

• On certain C⁰-aspects of contactomorphism groups
• There exist no contact Anosov diffeomorphisms
• Applications of square roots of diffeomorphisms
• The Group of Contact Diffeomorphisms for Compact Contact Manifolds
• Partially ordered groups and geometry of contact transformations