The Atiyah conjecture and \(L^2\)-cohomology computations

DOI10.1007/s10711-017-0293-2zbMath1496.20068OpenAlexW2765393749MaRDI QIDQ1663789

Kevin Schreve, Wiktor J. Mogilski

Publication date: 23 August 2018

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

Full work available at URL: https://doi.org/10.1007/s10711-017-0293-2

zbMATH Keywords

Coxeter groupsspecial groupsSinger conjecturestrong Atiyah conjecture\(L^2\)-Betti numbers

Mathematics Subject Classification ID

Geometric group theory (20F65) Cohomology of groups (20J06) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Hyperbolic groups and nonpositively curved groups (20F67)

Cites Work

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• The fattened Davis complex and weighted \(L^2\)-(co)homology of Coxeter groups
• The \(L^2\)-(co)homology of groups with hierarchies
• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).
• Buildings with isolated subspaces and relatively hyperbolic Coxeter groups.
• Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products.
• The topology of isospectral manifolds of tridiagonal matrices
• Weighted \(L^2\)-cohomology of Coxeter groups.
• Groups with the same cohomology as their profinite completions.
• Coxeter groups are virtually special
• Some aspherical manifolds
• Galois Cohomology
• Vanishing theorems and conjectures for the 2-homology of right-angled Coxeter groups
• Introduction to \(\ell_2\)-methods in topology: Reduced \(\ell_2\)-homology, harmonic chains, \(\ell_2\)-Betti numbers
• \(L^ 2\)-topological invariants of 3-manifolds
• \(\ell^2\)-homology of right-angled Coxeter groups based on barycentric subdivisions
• Special cube complexes
• Thin buildings.
• The strong Atiyah conjecture for virtually cocompact special groups
• Incoherent Coxeter Groups
• Rational group ring elements with kernels having irrational dimension
• Division Rings and Group von Neumann Algebras
• Coxeter Groups act on CAT(0) cube complexes

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