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

D. Gaboriau, R. Lyons

Inventiones Mathematicae, 177 (2009), 533--540.

DOI:    10.1007/s00222-009-0187-5
The original publication is available at www.springerlink.com

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Also HAL (CNRS) http://hal.archives-ouvertes.fr/hal-00186658/  or ArXiV http://fr.arxiv.org/abs/0711.1643


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.