On Turing dynamical systems and the Atiyah problem

DOI10.1007/s00222-013-0497-5zbMath1354.20026arXiv1004.2030OpenAlexW2159039200MaRDI QIDQ464825

Łukasz Grabowski

Publication date: 30 October 2014

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.2030

zbMATH Keywords

Turing machineslamplighter groupintegral group rings\(l^2\)-Betti numbers

Mathematics Subject Classification ID

Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Geometric group theory (20F65) Ergodic theorems, spectral theory, Markov operators (37A30) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05)

Related Items (16)

\(L^2\)-Betti numbers arising from the lamplighter group ⋮ Mean dimension, mean rank, and von Neumann-Lück rank ⋮ Approximating the group algebra of the lamplighter by infinite matrix products ⋮ Closed manifolds with transcendentalL²-Betti numbers: ⋮ The base change in the Atiyah and the Lück approximation conjectures ⋮ The Realization Problem for some wild monoids and the Atiyah Problem ⋮ L 2 -Betti numbers and computability of reals ⋮ On computing homology gradients over finite fields ⋮ The lamplighter group of rank two generated by a bireversible automaton ⋮ Group ring elements with large spectral density ⋮ On the center-valued Atiyah conjecture for \(L^2\)-Betti numbers ⋮ Dyson's spike for random Schroedinger operators and Novikov-Shubin invariants of groups ⋮ Random walks on graphs and approximation of \(L^2\)-invariants ⋮ 𝐾-theory for generalized Lamplighter groups ⋮ Vanishing of l²‐cohomology as a computational problem ⋮ Spectra of Cayley graphs of the lamplighter group and random Schrödinger operators

Cites Work

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