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.