The limit of $\mathbb{F}_{p}$-Betti numbers of a tower of finite covers with amenable fundamental groups

DOI10.1090/S0002-9939-2010-10689-5zbMath1272.55006arXiv1003.0434OpenAlexW2963096067MaRDI QIDQ3082311

Wolfgang Lück, Peter A. Linnell, Roman Sauer

Publication date: 10 March 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.0434

zbMATH Keywords

amenabilityBetti numbersOre localization

Mathematics Subject Classification ID

Homotopy theory (55P99) Homology and cohomology theories in algebraic topology (55N99) Means on groups, semigroups, etc.; amenable groups (43A07) Ore rings, multiplicative sets, Ore localization (16U20)

Related Items (7)

Growth of mod-2 homology in higher-rank locally symmetric spaces ⋮ Approximating \(L^2\)-invariants and homology growth ⋮ On computing homology gradients over finite fields ⋮ Homology growth, hyperbolization, and fibering ⋮ Exponential growth of torsion in abelian coverings ⋮ Volume gradients and homology in towers of residually-free groups ⋮ Connes embeddings and von Neumann regular closures of amenable group algebras

Cites Work

• The strong approximation conjecture holds for amenable groups
• A short proof of the approximation conjecture for amenable groups
• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Amenable groups, topological entropy and Betti numbers
• Mean topological dimension
• Applications of a New K-Theoretic Theorem to Soluble Group Rings
• The rank of finitely generated modules over group algebras
• Approximating L²‐invariants and the Atiyah conjecture
• Expansive algebraic actions of discrete residually finite amenable groups and their entropy
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