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

2020/09/22 by Philip Möller, Möller, Philip, Olga Varghese +1
Mathematics · #Advanced Topology and Set Theory #Advanced Operator Algebra Research #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2009.10470

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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