Abstract group actions of locally compact groups on CAT(0) spaces
Group Theory
2021-02-18 v2
Abstract
We study abstract group actions of locally compact Hausdorff groups on CAT(0) spaces. Under mild assumptions on the action we show that it is continuous or has a global fixed point. This mirrors results by Dudley and Morris-Nickolas for actions on trees. As a consequence we obtain a geometric proof for the fact that any abstract group homomorphism from a locally compact Hausdorff group into a torsion free CAT(0) group is continuous.
Keywords
Cite
@article{arxiv.2009.10470,
title = {Abstract group actions of locally compact groups on CAT(0) spaces},
author = {Philip Möller and Olga Varghese},
journal= {arXiv preprint arXiv:2009.10470},
year = {2021}
}
Comments
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