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

[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.

[学科分类] 神经科学

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