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.
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