Amenable covers, volume and L 2-Betti numbers of aspherical manifolds

DOI10.1515/CRELLE.2009.082zbMath1188.55003arXivmath/0605627OpenAlexW2962931334MaRDI QIDQ3404362

Roman Sauer

Publication date: 9 February 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605627

zbMATH Keywords

minimal volumeaspherical manifolds\(L^2\)-Betti numbersRicci curvature bounded below\(\mathcal{R}\)-simplicial complexesfoliated simplicial volumefoliated singular homologymeasurable group theorysupport mass

Mathematics Subject Classification ID

Equivariant homology and cohomology in algebraic topology (55N91) Foliations in differential topology; geometric theory (57R30) Other homology theories in algebraic topology (55N35) Singular homology and cohomology theory (55N10) Homology with local coefficients, equivariant cohomology (55N25) Products and intersections in homology and cohomology (55N45)

Related Items (13)

Volume and macroscopic scalar curvature ⋮ Integral foliated simplicial volume and \(S^1\)-actions ⋮ On the simplicial volume and the Euler characteristic of (aspherical) manifolds ⋮ Amenable covers and integral foliated simplicial volume ⋮ Amenable category and complexity ⋮ Minimal volume entropy of RAAG's ⋮ Amenable covers of right‐angled Artin groups ⋮ Coarse flow spaces for relatively hyperbolic groups ⋮ L2-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices ⋮ Equivariant covers for hyperbolic groups. ⋮ Integral foliated simplicial volume of aspherical manifolds ⋮ Variations on the theme of the uniform boundary condition ⋮ Gromov’s Theory of Multicomplexes with Applications to Bounded Cohomology and Simplicial Volume

Cites Work

• \(L_ 2\)-cohomology and group cohomology
• Entropy and isomorphism theorems for actions of amenable groups
• On the Busemann-Petty problem for perturbations of the ball
• De Rham-Hodge theory for \(L^2\)-cohomology of infinite coverings
• Von Neumann categories and extended \(L^2\)-cohomology
• On asymptotic dimension of groups acting on trees.
• Lower bounds on Ricci curvature and the almost rigidity of warped products
• Gromov's measure equivalence and rigidity of higher rank lattices
• Orbit equivalence rigidity
• Homological invariants and quasi-isometry.
• Groups of Automorphisms of Borel Spaces

This page was built for publication: Amenable covers, volume and L 2-Betti numbers of aspherical manifolds