A Measurable-Group-Theoretic Solution to von Neumann's Problem
arXiv:0711.1643
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.
10 pages, to appear in Inventiones Mathematicae