English

A Measurable-Group-Theoretic Solution to von Neumann's Problem

Group Theory 2009-03-11 v2 Dynamical Systems Operator Algebras Probability

Abstract

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.

Keywords

Cite

@article{arxiv.0711.1643,
  title  = {A Measurable-Group-Theoretic Solution to von Neumann's Problem},
  author = {Damien Gaboriau and Russell Lyons},
  journal= {arXiv preprint arXiv:0711.1643},
  year   = {2009}
}

Comments

10 pages, to appear in Inventiones Mathematicae

R2 v1 2026-06-21T09:42:15.814Z