Volume 17, issue 2 (2013)

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Betti numbers of finite volume orbifolds

Iddo Samet

Geometry & Topology 17 (2013) 1113–1147
Abstract

We prove that the Betti numbers of a negatively curved orbifold are linearly bounded by its volume, generalizing a theorem of Gromov that establishes this bound for manifolds. An immediate corollary is that Betti numbers of a lattice in a rank-one Lie group are linearly bounded by its co-volume.

Keywords
orbifolds, homology, Betti numbers, negative curvature
Mathematical Subject Classification 2010
Primary: 53C20
References
Publication
Received: 27 September 2011
Accepted: 29 October 2012
Published: 7 May 2013
Proposed: Walter Neumann
Seconded: Dmitri Burago, John Lott
Authors
Iddo Samet
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Chicago, IL 60607
USA