Characterization of the Fundamental Group of a Differentiable Manifold by the Action of Its Group of Diffeomorphisms

摘要

Let X be a connected differentiable manifold and Diff(X) the corresponding group of diffeomorphisms. Starting from a construction of the universal covering space of the neutral component of Diff(X) we establish that the fundamental group of X is isomorphic with the group of components of the isotropy subgroup of a point under the transitive action of this covering on X. (ERA citation 07:058549)