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International Mathematics Research Notices Advance Access originally published online on June 19, 2009
International Mathematics Research Notices (2009) 2009:4220-4231, doi:10.1093/imrn/rnp085 published on October 27, 2009
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

L2-Betti Numbers and Non-Unitarizable Groups without Free Subgroups

Denis V. Osin

Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA

Correspondence: Correspondence to be sent to: denis.osin{at}gmail.com

We show that there exist non-unitarizable groups without nonabelian free subgroups. Both torsion and torsion free examples are constructed. As a by-product, we show that there exist finitely generated torsion groups with nonvanishing first L2-Betti numbers. We also relate the well-known problem of whether every hyperbolic group is residually finite to an open question about approximation of L2-Betti numbers.

Communicated by Prof. Marc Burger


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