L2-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices

DOI10.1112/topo.12056zbMath1388.22008arXiv1612.04559OpenAlexW2581144387MaRDI QIDQ4637524

Andreas Thom, Henrik Densing Petersen, Roman Sauer

Publication date: 24 April 2018

Published in: Journal of Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.04559

zbMATH Keywords

\(L^2\)-Betti numbersFarber sequenceuniformly discrete lattices

Mathematics Subject Classification ID

Homology and cohomology theories in algebraic topology (55N99) Locally compact groups and their algebras (22D99)

Related Items (7)

Invariant random subgroups over non-Archimedean local fields ⋮ A note on the rational homological dimension of lattices in positive characteristic ⋮ \(\ell^2\)-Betti numbers of random rooted simplicial complexes ⋮ Asymptotic invariants of lattices in locally compact groups ⋮ Complete group rings as Hecke algebras ⋮ Characters, \(L^2\)-Betti numbers and an equivariant approximation theorem ⋮ Rational discrete first degree cohomology for totally disconnected locally compact groups

Cites Work

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• \(L^2\)-Betti numbers of locally compact groups
• On the growth of Betti numbers of locally symmetric spaces
• Group cocycles and the ring of affiliated operators
• Finiteness properties of arithmetic groups over function fields.
• Weighted \(L^2\)-cohomology of Coxeter groups.
• Volumes of S-arithmetic quotients of semi-simple groups. With an appendix by Moshe Jarden and Gopal Prasad
• Lattices of minimum covolume in Chevalley groups over local fields of positive characteristic
• Low degree bounded cohomology and \(L^{2}\)-invariants for negatively curved groups
• Transformation groups
• Die Kohomologie S-arithmetischer Gruppen über Funktionenkörpern
• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Geometry of growth: approximation theorems for \(L^2\) invariants
• Invariant random subgroups over non-Archimedean local fields
• Kazhdan-Margulis theorem for invariant random subgroups
• \(\ell^2\) invariants of equivalence relations and groups
• Asymptotics of Betti numbers, \(l^ 2\)-invariants and laminations
• \(L^2\)-Betti numbers and Plancherel measure
• On the growth of \(L^2\)-invariants for sequences of lattices in Lie groups
• \(L^{2}\)-cohomology for von Neumann algebras
• Invariant percolation and harmonic Dirichlet functions
• Thin buildings.
• Weak Notions of Normality and Vanishing up to Rank in L2-Cohomology
• Simple groups without lattices
• L²-BETTI NUMBERS OF DISCRETE MEASURED GROUPOIDS
• Amenable covers, volume and L 2-Betti numbers of aspherical manifolds
• A spectral sequence to compute L ² -Betti numbers of groups and groupoids
• Topological Models of Finite Type for Tree Almost Automorphism Groups
• L2-Betti number of discrete and non-discrete groups
• 𝐿²-Betti numbers of locally compact groups and their cross section equivalence relations
• Hyperlinear and Sofic Groups: A Brief Guide

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