On computing homology gradients over finite fields

DOI10.1017/S0305004116000657zbMath1375.22006arXiv1410.1693OpenAlexW176131108MaRDI QIDQ5360445

Łukasz Grabowski, Thomas Schick

Publication date: 28 September 2017

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

Full work available at URL: https://arxiv.org/abs/1410.1693

zbMATH Keywords

universal coverAtiyah conjecturefinite \(CW\)-complex\(l^2\)-Betti numberhomology gradient

Mathematics Subject Classification ID

Covering spaces and low-dimensional topology (57M10) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Extensions, wreath products, and other compositions of groups (20E22) Group algebras of locally compact groups (22D15)

Cites Work

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• On Turing dynamical systems and the Atiyah problem
• On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper's operator
• Rank gradient, cost of groups and the rank versus Heegaard genus problem
• The strong approximation conjecture holds for amenable groups
• On the spectrum of lamplighter groups and percolation clusters
• \(L_ 2\)-cohomology and group cohomology
• Entropy and isomorphism theorems for actions of amenable groups
• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Geometry of growth: approximation theorems for \(L^2\) invariants
• Introduction to \(\ell_2\)-methods in topology: Reduced \(\ell_2\)-homology, harmonic chains, \(\ell_2\)-Betti numbers
• The spectral measure of certain elements of the complex group ring of a wreath product
• Irrational \(l^2\) invariants arising from the lamplighter group
• On a question of Atiyah
• Free lamplighter groups and a question of Atiyah
• Arbitrary p-gradient values
• Rational group ring elements with kernels having irrational dimension
• The limit of $\mathbb{F}_{p}$-Betti numbers of a tower of finite covers with amenable fundamental groups
• Sofic representations of amenable groups
• Closed manifolds with transcendentalL²-Betti numbers:
• Large groups, property (τ) and the homology growth of subgroups
• Division Rings and Group von Neumann Algebras
• Approximating L²‐invariants and the Atiyah conjecture
• The lamplighter group as a group generated by a 2-state automaton, and its spectrum