Boundary amenability of relatively hyperbolic groups

被引：26

作者：

Ozawa, Narutaka ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[2] Univ Tokyo, Dept Math Sci, Komaba 1538914, Japan

来源：

TOPOLOGY AND ITS APPLICATIONS | 2006年 / 153卷 / 14期

基金：

日本学术振兴会;

关键词：

fine hyperbolic graph; relatively hyperbolic groups; exactness; amenable action;

D O I：

10.1016/j.topol.2005.11.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let K be a fine hyperbolic graph and Gamma be a group acting on K with finite quotient. We prove that Gamma 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 Gamma 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. (C) 2005 Elsevier B.V. All rights reserved.

引用

页码：2624 / 2630

页数：7

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