## Journal of Symplectic Geometry

### The group of contact diffeomorphisms for compact contact manifolds

#### Abstract

For a compact contact manifold $M^{2n + 1}$, it is shown that the anisotropic Folland-Stein function spaces $\Gamma^{s} (M), s \geq (2n + 4)$ form an algebra. The notion of anisotropic regularity is extended to define the space of $\Gamma^{s}$-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 analyse the action of the group of contact diffeomorphisms on the space of CR structures on a compact, three-dimensional manifold.

#### Article information

Source
J. Symplectic Geom., Volume 12, Number 1 (2014), 49-104.

Dates
First available in Project Euclid: 29 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1409317364

Mathematical Reviews number (MathSciNet)
MR3194076

Zentralblatt MATH identifier
1302.53045

#### Citation

Bland, John; Duchamp, Tom. The group of contact diffeomorphisms for compact contact manifolds. J. Symplectic Geom. 12 (2014), no. 1, 49--104. https://projecteuclid.org/euclid.jsg/1409317364