局部紧群在局部可缩空间上的传递作用
群论
2013-07-23 v4 一般拓扑
摘要
假设 是局部紧群模去一个闭子群的商空间。如果 是局部可缩且连通的，我们证明 是一个流形。如果 -作用是忠实的，则 是一个 Lie 群。
引用
@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}
}
备注
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