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A Measurable-Group-Theoretic Solution to von Neumann's Problem (2007)

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.

Publication details
Download http://hal.archives-ouvertes.fr/hal-00186658/en/
Publisher HAL - CCSD
Repository CCSd/HAL : e-articles server (based on gBUS) (France)
Keywords Mathematics/Group Theory, Mathematics/Probability, Mathematics/Operator Algebras, Mathematics/Dynamical Systems, Orbit equivalence, free group, non-amenability, von Neumann's problem, percolation theory, graphs, trees
Type text
Language English
Relation http://hal.archives-ouvertes.fr/docs/00/36/73/03/PDF/Gaboriau-Lyons-v2.pdf