The strong Atiyah conjecture for right-angled Artin and Coxeter groups.

DOI10.1007/s10711-011-9631-yzbMath1275.20042arXiv1010.0606OpenAlexW2068996638MaRDI QIDQ431056

Thomas Schick, Peter A. Linnell, Boris L. Okun

Publication date: 26 June 2012

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.0606

zbMATH Keywords

orders of finite subgroupsBetti numbersright-angled Artin groupsright-angled Coxeter groupsresidually torsion-free nilpotent groupsstrong Atiyah conjecture

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Geometric group theory (20F65) Braid groups; Artin groups (20F36) Cohomology of groups (20J06) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Topological methods in group theory (57M07) Residual properties and generalizations; residually finite groups (20E26) Homology with local coefficients, equivariant cohomology (55N25)

Related Items (9)

A combination theorem for cubulation in small cancellation theory over free products ⋮ Localization, Whitehead groups and the Atiyah conjecture ⋮ Rips construction without unique product ⋮ Profinite properties of RAAGs and special groups ⋮ On the center-valued Atiyah conjecture for \(L^2\)-Betti numbers ⋮ The strong Atiyah conjecture for virtually cocompact special groups ⋮ The Bieri-Neumann-Strebel invariants via Newton polytopes ⋮ The pure cactus group is residually nilpotent ⋮ Rips-Segev torsion-free groups without the unique product property

Cites Work

• Unnamed Item
• Groups with the same cohomology as their pro-\(p\) completions.
• The lower central series of the free partially commutative group
• Vanishing theorems and conjectures for the 2-homology of right-angled Coxeter groups
• Integrality of \(L^2\)-Betti numbers
• Right-angled Artin groups are commensurable with right-angled Coxeter groups
• Rational group ring elements with kernels having irrational dimension
• Closed manifolds with transcendentalL²-Betti numbers:
• Finite group extensions and the Atiyah conjecture
• Division Rings and Group von Neumann Algebras
• Approximating L²‐invariants and the Atiyah conjecture

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