Transitive actions of locally compact groups on locally contractible spaces

Karl H. Hofmann; Linus Kramer

Transitive actions of locally compact groups on locally contractible spaces

Group Theory 2013-07-23 v4 General Topology

Authors: Karl H. Hofmann , Linus Kramer

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.

Keywords

locally compact group locally contractible space transitive action Lie group manifold

Cite

@article{arxiv.1301.5114,
  title  = {Transitive actions of locally compact groups on locally contractible spaces},
  author = {Karl H. Hofmann and Linus Kramer},
  journal= {arXiv preprint arXiv:1301.5114},
  year   = {2013}
}

Comments

Minor 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

Transitive actions of locally compact groups on locally contractible spaces

Abstract

Keywords

Cite

Comments

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