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- Title
L2-Betti Numbers and Non-Unitarizable Groups without Free Subgroups.
- Authors
Osin, Denis V.
- Abstract
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.
- Subjects
UNITARY operators; SUBGROUP growth; APPROXIMATION theory; NUMERICAL analysis; GROUP theory
- Publication
IMRN: International Mathematics Research Notices, 2009, Vol 2009, Issue 22, p4220
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnp085