Self-diffeomorphism group

Definition
The self-diffeomorphism group of a differential manifold is defined in any of the following equivalent ways:


 * It is the group whose elements are diffeomorphisms from the differential manifold to itself, and where multiplication is by composition
 * It is the automorphism group of the differential manifold, viewed as an object in the category of differential manifolds with smooth maps

Facts

 * The self-diffeomorphism group of a differential manifold acts transitively on the manifold.
 * The self-diffeomorphism group is a subgroup of the self-homeomorphism group. It is often a conjugate-dense subgroup and often is also a finite-dominating subgroup.