A measurable-group-theoretic solution to von Neumann's problem

被引：60

作者：

Gaboriau, Damien ^{[1
]}

Lyons, Russell ^{[2
]}

机构：

[1] Univ Lyon, Unite Math Pures & Appl, CNRS, Ens Lyon, F-69364 Lyon 7, France

[2] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

来源：

INVENTIONES MATHEMATICAE | 2009年 / 177卷 / 03期

关键词：

MINIMAL SPANNING FORESTS; CAYLEY-GRAPHS; PERCOLATION; EQUIVALENCE; CLUSTERS; COST;

D O I：

10.1007/s00222-009-0187-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group von Neumann factor into restricted wreath product factors.

引用

页码：533 / 540

页数：8

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