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

Philip Möller; Olga Varghese

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arXiv · 2009.10470

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

Philip Möller·Olga Varghese

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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.

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Philip Möller, Olga Varghese. 2020-09-22. Abstract group actions of locally compact groups on CAT(0) spaces. https://arxiv.org/abs/2009.10470

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