Coarse non-amenability and covers with small eigenvalues.

DOI10.1007/s00208-011-0759-8zbMath1270.20041arXiv1009.1966OpenAlexW2158549157MaRDI QIDQ1938425

Erik Guentner, Goulnara N. Arzhantseva

Publication date: 4 February 2013

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1966

zbMATH Keywords

Cayley graphsfree groupsresidually finite groupsamenable groupsCheeger constantsclosed Riemannian manifoldseigenvalue of the Laplacianfiltrations by characteristic subgroupsfiltrations of groups with subgroups of finite indextowers of finite sheeted regular covers

Mathematics Subject Classification ID

Covering spaces and low-dimensional topology (57M10) Geometric group theory (20F65) Global Riemannian geometry, including pinching (53C20) Asymptotic properties of groups (20F69) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (3)

Expanders and box spaces ⋮ From the geometry of box spaces to the geometry and measured couplings of groups ⋮ On a family of representations of residually finite groups

Cites Work

• Volume and bounded cohomology
• The spectral geometry of a tower of coverings
• Riemannian coverings and isospectral manifolds
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• Surface subgroups of Kleinian groups with torsion
• Remarks on Yu’s ‘property A’ for discrete metric spaces and groups
• The first eigenvalue in a tower of coverings
• Small eigenvalues of the Laplace operator on compact Riemann surfaces
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