Uniform non-amenability, cost, and the first \(\ell^2\)-Betti number

DOI10.4171/GGD/49zbMath1196.37011arXiv0711.0393MaRDI QIDQ955219

Russell Lyons, Stéphane Vassout, Mikaël Pichot

Publication date: 19 November 2008

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.0393

zbMATH Keywords

\(\ell^2\)-Betti numbersmeasured equivalence relationsuniform non-amenability

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Geometric group theory (20F65) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (3)

Exponential growth rates of free and amalgamated products. ⋮ \(C^*\)-simple groups without free subgroups ⋮ The Tarski numbers of groups

Cites Work

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• \(L_ 2\)-cohomology and group cohomology
• Uniform spanning forests
• Uniform non-amenability
• An amenable equivalence relation is generated by a single transformation

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