The Group of Contact Diffeomorphisms for Compact Contact Manifolds

2010/07/13 by John Bland, Bland, John, Tom Duchamp +1
Mathematics · #32G05 (secondary) #58D05 (primary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:32G05 #msc:58D05

paper · pdf · doi:10.48550/arxiv.1007.2036

41 pages

arxiv created 2010/07/13 · arxiv updated 2010/07/14

Abstract

For a compact contact manifold it is shown that the anisotropic Folland-Stein function spaces form an algebra. The notion of anisotropic regularity is extended to define the space of Folland-Stein contact diffeomorphisms, which is shown to be a topological group under composition and a smooth Hilbert manifold. These results are used in a subsequent paper to analyze the action of the group of contact diffeomorphisms on the space of CR structures on a compact, three dimensional manifold.

Related

• The space of Cauchy-Riemann structures on 3-D compact contact manifolds
• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• On transitive contact and CR algebras
• Sur les transformations de contact au-dessus des surfaces
• Geometry of the contactomorphism group