CAT（0）空间上局部紧群的抽象群作用

Pub Date : 2020-09-22 DOI:10.4171/ggd/677

Philip Moller, Olga Varghese

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引用次数: 2

摘要

研究了CAT(0)空间上局部紧Hausdorff群的抽象群作用。在对作用的温和假设下，我们证明了它是连续的或有一个全局不动点。这反映了达德利和莫里斯-尼古拉斯对树木行为的研究结果。由此，我们得到了从局部紧Hausdorff群到无扭转CAT(0)群的任何抽象群同态是连续的一个几何证明。

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Abstract group actions of locally compact groups on CAT(0) spaces

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.

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