论文标题
CAT（0）空间上本地紧凑组的抽象组动作
Abstract group actions of locally compact groups on CAT(0) spaces
论文作者
论文摘要
我们研究了CAT（0）空间上局部紧凑的Hausdorff组的抽象组动作。在对动作的轻度假设下，我们表明它是连续的或具有全球固定点。这反映了达德利（Dudley）和莫里斯·尼古拉斯（Morris Nickolas）在树上的作用。结果，我们获得了一个几何证据，因为任何抽象组从局部紧凑的Hausdorff组中的任何抽象群体同态转变为无扭力的CAT（0）组都是连续的。
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.
