Cheeger constants and \(L^2\)-Betti numbers

DOI10.1215/00127094-2871415zbMath1312.57041arXiv1303.5963OpenAlexW2147009572MaRDI QIDQ2339644

Lewis Phylip Bowen

Publication date: 2 April 2015

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5963

zbMATH Keywords

hyperbolic manifoldCheeger constant\(L^2\)-Betti numbers

Mathematics Subject Classification ID

Homogeneous spaces (22F30) Discontinuous groups of transformations (57S30)

Related Items

Benjamini-Schramm convergence and spectra of random hyperbolic surfaces of high genus ⋮ Equivariant Benjamini–Schramm convergence of simplicial complexes and ℓ2-multiplicities ⋮ Convergence of normalized Betti numbers in nonpositive curvature ⋮ \(\ell^2\)-Betti numbers of random rooted simplicial complexes ⋮ Locally compact sofic groups ⋮ A volume comparison theorem for characteristic numbers ⋮ All finitely generated Kleinian groups of small Hausdorff dimension are classical Schottky groups ⋮ Unimodular measures on the space of all Riemannian manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Kleinian groups of small Hausdorff dimension are classical Schottky groups. I
• The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups
• On the bass note of a Schottky group
• Indecomposability of treed equivalence relations
• Hausdorff dimensions of limit sets. I
• Compact 3-manifolds of constant negative curvature fibering over the circle
• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Hausdorff dimension and Kleinian groups
• Related aspects of positivity in Riemannian geometry
• Recurrence of distributional limits of finite planar graphs
• \(\ell^2\) invariants of equivalence relations and groups
• Topics in orbit equivalence
• On the growth of \(L^2\)-invariants for sequences of lattices in Lie groups
• Processes on unimodular random networks
• Invariant percolation and harmonic Dirichlet functions
• Betti numbers are testable
• Ergodic theory of amenable group actions. I: The Rohlin lemma
• A note on the isoperimetric constant
• Limit sets of discrete groups of isometries of exotic hyperbolic spaces
• Characterizing the 3-cell by its metric
• Compact Submanifolds of 3-Manifolds
• On the imbedding of systems of compacta in simplicial complexes
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu