Transitive actions of locally compact groups on locally contractible spaces

Abstract

Suppose that $X=G/K$ is the quotient of a locally compact group by a closed subgroup. If $X$ is locally contractible and connected, we prove that $X$ is a manifold. If the $G$-action is faithful, then $G$ is a Lie group.

arXiv commentMinor corrections in v2 an in v3. The proof of Lemma 3.4 was incorrect in v1 - v3. A correct proof is now given in a separate erratum at the end of the article. Both the article and the erratum will appear in Crelle Journal Reine Angew. Mathematik