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A measurable-group-theoretic solution to von Neumann’s problem

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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.

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Authors and Affiliations

  1. Unité de Mathématiques Pures et Appliquées, Université de Lyon, CNRS, Ens-Lyon, 46, allée d’Italie, 69364, Lyon cedex 7, France

    Damien Gaboriau

  2. Department of Mathematics, Indiana University Bloomington, Bloomington, IN, 47405-5701, USA

    Russell Lyons

Authors
  1. Damien Gaboriau
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  2. Russell Lyons
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Correspondence to Damien Gaboriau.

Additional information

D. Gaboriau’s research was supported by CNRS.

R. Lyons’ research was supported partially by NSF grant DMS-0705518 and Microsoft Research.

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Gaboriau, D., Lyons, R. A measurable-group-theoretic solution to von Neumann’s problem. Invent. math. 177, 533–540 (2009). https://doi.org/10.1007/s00222-009-0187-5

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  • DOI: https://doi.org/10.1007/s00222-009-0187-5

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