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

Groups, geometry, and dynamics

article

Philip Möller¹  Olga Varghese² 

[1] University of Münster;Otto-von-Guericke University Magdeburg

关键词: Automatic continuity;    locally compact groups;    CAT(0) spaces;   

DOI  :  10.4171/ggd/677

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

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.

【 授权许可】

CC BY