The Group of Contact Diffeomorphisms for Compact Contact Manifolds

TL;DR

This paper establishes that the space of Folland-Stein contact diffeomorphisms on a compact contact manifold forms a smooth topological group and a Hilbert manifold, enabling advanced analysis of CR structures.

Contribution

It introduces the Folland-Stein contact diffeomorphism group as a smooth Hilbert manifold and proves its topological group structure on compact contact manifolds.

Findings

Folland-Stein spaces form an algebra on compact contact manifolds

The contact diffeomorphism space is a topological group

The space of contact diffeomorphisms is a smooth Hilbert manifold

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.