On the center-valued Atiyah conjecture for \(L^2\)-Betti numbers

zbMath1376.46053arXiv1605.09069MaRDI QIDQ526156

Anselm Knebusch, Thomas Schick, Peter A. Linnell

Publication date: 10 May 2017

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.09069

zbMATH Keywords

von Neumann dimensionAtiyah conjecture\(L^2\)-Betti numberscenter-valued trace

Mathematics Subject Classification ID

Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) (K)-theory and operator algebras (including cyclic theory) (46L80) General theory of von Neumann algebras (46L10) Linear operator approximation theory (47A58)

Related Items (1)

Universality of free random variables: atoms for non-commutative rational functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).
• The strong Atiyah conjecture for right-angled Artin and Coxeter groups.
• The Atiyah conjecture and Artinian rings.
• On Turing dynamical systems and the Atiyah problem
• Brauer induction for \(G_ 0\) of certain infinite groups
• Hilbert modules and modules over finite von Neumann algebras and applications to \(L^ 2\)-invariants
• Integrality of \(L^2\)-Betti numbers
• On the K- and L-theory of the algebra of operators affiliated to a finite von Neumann algebra
• Hyperlinearity, essentially free actions and \(L^2\)-invariants. The sofic property
• Special cube complexes
• The strong Atiyah conjecture for virtually cocompact special groups
• $L^2$-determinant class and approximation of $L^2$-Betti numbers
• Rational group ring elements with kernels having irrational dimension
• A boundary criterion for cubulation
• Closed manifolds with transcendentalL²-Betti numbers:
• Galois cohomology of completed link groups
• Finite group extensions and the Atiyah conjecture
• Division Rings and Group von Neumann Algebras
• Approximating L²‐invariants and the Atiyah conjecture
• Approximation of center-valued Betti-numbers

This page was built for publication: On the center-valued Atiyah conjecture for \(L^2\)-Betti numbers