APPROXIMATING THE FIRST L2-BETTI NUMBER OF RESIDUALLY FINITE GROUPS

DOI10.1142/S1793525311000532zbMath1243.20039arXiv1011.4739OpenAlexW2963559546MaRDI QIDQ3020557

Wolfgang Lück, Denis V. Osin

Publication date: 4 August 2011

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.4739

zbMATH Keywords

torsion groupsfinitely generated residually finite groups\(L^2\)-Betti numbersapproximation conjecture

Mathematics Subject Classification ID

Geometric group theory (20F65) Noncommutative topology (46L85) Residual properties and generalizations; residually finite groups (20E26)

Related Items (12)

On upper bounds for the first ℓ²-Betti number ⋮ Normal generation and \(\ell^2\)-Betti numbers of groups. ⋮ On acylindrical hyperbolicity of groups with positive first ℓ²-Betti number ⋮ On growth of homology torsion in amenable groups ⋮ \(C^*\)-simple groups without free subgroups ⋮ The Tarski numbers of groups ⋮ Volume gradients and homology in towers of residually-free groups ⋮ Acylindrical hyperbolicity of groups acting on trees ⋮ Cost, \(\ell^2\)-Betti numbers and the sofic entropy of some algebraic actions ⋮ Asymptotics of Cheeger constants and unitarisability of groups ⋮ Non-standard limits of graphs and some orbit equivalence invariants ⋮ Asymptotic invariants, complexity of groups and related problems

Cites Work

• Golod-Shafarevich groups with property \((T)\) and Kac-Moody groups.
• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Non-amenable finitely presented torsion-by-cyclic groups.
• Rank gradient and torsion groups

This page was built for publication: APPROXIMATING THE FIRST L²-BETTI NUMBER OF RESIDUALLY FINITE GROUPS