论文标题
猫（0）空间的边界动作及其$ C^*$ - 代数
Boundary actions of CAT(0) spaces and their $C^*$-algebras
论文作者
论文摘要
在本文中，我们从拓扑动力学和$ c^*$ - 代数的角度研究了猫（0）空间的边界动作。首先，我们研究了右角核群和右角artin组的作用，并在其自然分配的CAT（0）Cube Cuble配合物的视觉边界和Nevo-Sageev边界上具有有限的图形。特别是，我们通过研究相应的$ \ cat $ cube Complexs并确立了必要的动力学特性，例如这些动作的$ \ cat $ cube complectes（例如，纯粹的无限性结果$ c^*$ - 这些动作的代数），例如这些动作的最小化，拓扑和纯粹的无限性。此外，我们研究了基本图的基本群体对低音 - 塞雷树的视觉边界的作用。我们表明，可重复的路径的存在本质上意味着该动作为$ 2 $填充，从中，我们还获得了一大类的Unital Kirchberg代数。此外，我们的结果还提供了一种新方法来识别$ c^*$ - 简单的概括性baumslag-solitar群组。从我们的方法获得的群体的示例就\ cite {g-g-k-n}的意义上有$ n $偏二氧。该课程特别包含非二元的免费产品，鲍姆斯拉格 - s-solitar群组和$ n $ circles或$ n $ circles的基本组。
In this paper, we study boundary actions of CAT(0) spaces from a point of view of topological dynamics and $C^*$-algebras. First, we investigate the actions of right-angled Coexter groups and right-angled Artin groups with finite defining graphs on the visual boundaries and the Nevo-Sageev boundaries of their natural assigned CAT(0) cube complexes. In particular, we establish (strongly) pure infiniteness results for reduced crossed product $C^*$-algebras of these actions through investigating the corresponding $\cat$ cube complexes and establishing necessary dynamical properties such as minimality, topological freeness and pure infiniteness of the actions. In addition, we study actions of fundamental groups of graphs of groups on the visual boundaries of their Bass-Serre trees. We show that the existence of repeatable paths essentially implies that the action is $2$-filling, from which, we also obtain a large class of unital Kirchberg algebras. Furthermore, our result also provides a new method in identifying $C^*$-simple generalized Baumslag-Solitar groups. The examples of groups obtained from our method have $n$-paradoxical towers in the sense of \cite{G-G-K-N}. This class particularly contains non-degenerated free products, Baumslag-Solitar groups and fundamental groups of $n$-circles or wedge sums of $n$-circles.
