Boundary amenability of relatively hyperbolic groups
Boundary amenability of relatively hyperbolic groups
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DOI：
10.1016/j.topol.2005.11.001
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发表时间：
2005-01
影响因子：
0.6
通讯作者：
N. Ozawa
中科院分区：
文献类型：
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作者：
N. Ozawa
令 K 为精细双曲线图，且 Γ 为作用于 K 的有限商群。我们证明，如果所有顶点稳定器都是精确的，则 Γ 是精确的。特别是，如果一个相对双曲群的所有外围群都是精确的，那么它就是精确的。我们通过证明群 Γ 在紧拓扑空间上表现得很好来证明这一点。我们包括冯诺依曼代数群和可测量轨道等价关系理论的一些应用。
Let K be a fine hyperbolic graph and Γ be a group acting on K with finite quotient. We prove that Γ is exact provided that all vertex stabilizers are exact. In particular, a relatively hyperbolic group is exact if all its peripheral groups are exact. We prove this by showing that the group Γ acts amenably on a compact topological space. We include some applications to the theories of group von Neumann algebras and of measurable orbit equivalence relations.