Amenable covers, volume and L2-Betti numbers of aspherical manifolds

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dc.creatorSauer, Roman
dc.date2006-05-23
dc.date2008-06-30
dc.date.accessioned2026-07-07T09:47:15Z
dc.date.available2026-07-07T09:47:15Z
dc.descriptionWe provide a proof for an inequality between volume and L2-Betti numbers of aspherical manifolds for which Gromov outlined a strategy based on general ideas of Connes. The implementation of that strategy involves measured equivalence relations, Gaboriau's theory of L2-Betti numbers of R-simplicial complexes, and other themes of measurable group theory. Further, we prove new vanishing theorems for L2-Betti numbers that generalize a classical result of Cheeger and Gromov. As one of the corollaries, we obtain a gap theorem which implies vanishing of L2-Betti numbers of an aspherical manifold when its minimal volume is sufficiently small.
dc.descriptionminor corrections; to appear in J. Reine Angew. Math (Crelle)
dc.identifierhttps://arxiv.org/abs/math/0605627
dc.identifierhttp://arxiv.org/abs/math/0605627
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163806
dc.subjectAlgebraic Topology
dc.subjectDifferential Geometry
dc.subjectDynamical Systems
dc.subject22D20; 53C20; 58J22
dc.titleAmenable covers, volume and L2-Betti numbers of aspherical manifolds
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