Betti numbers of finite volume orbifolds

Samet, Iddo

doi:10.2140/gt.2013.17.1113

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Betti numbers of finite volume orbifolds

Iddo Samet

Geometry & Topology 17 (2013) 1113–1147

DOI: 10.2140/gt.2013.17.1113

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

Volume 17, issue 2 (2013)