Equivariant Benjamini–Schramm convergence of simplicial complexes and ℓ2-multiplicities

DOI10.1142/S1793525321500126MaRDI QIDQ5072108

Michael Schrödl-Baumann, Steffen Kionke

Publication date: 25 April 2022

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

Full work available at URL: https://arxiv.org/abs/1905.05658

zbMATH Keywords

Benjamini-Schramm convergenceunimodular measures\( \ell^2\)-invariantsinduction operationsofic sequences

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Covering spaces and low-dimensional topology (57M10) Finite transformation groups (57S17) Other homology theories in algebraic topology (55N35) Equivariant PL-topology (57Q91)

Cites Work

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• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Characters, \(L^2\)-Betti numbers and an equivariant approximation theorem
• Recurrence of distributional limits of finite planar graphs
• \(\ell^2\)-Betti numbers of random rooted simplicial complexes
• Cheeger constants and \(L^2\)-Betti numbers
• Processes on unimodular random networks
• $L^2$-determinant class and approximation of $L^2$-Betti numbers
• Betti numbers are testable
• Approximating L²‐invariants and the Atiyah conjecture

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