On the virtual Betti numbers of arithmetic hyperbolic 3–manifolds

Cooper, Daryl; Long, Darren; Reid, Alan W

doi:10.2140/gt.2007.11.2265

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On the virtual Betti numbers of arithmetic hyperbolic $3$–manifolds

D Cooper, D D Long and A W Reid

Geometry & Topology 11 (2007) 2265–2276

DOI: 10.2140/gt.2007.11.2265

Abstract

We show that closed arithmetic hyperbolic 3–manifolds with virtually positive first Betti number have infinite virtual first Betti number. As a consequence, such manifolds have large fundamental group.

Keywords

virtual Betti number, large fundamental group

Mathematical Subject Classification 2000

Primary: 57M10

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Publication

Received: 13 December 2006

Accepted: 5 September 2007

Published: 17 December 2007

Proposed: Dave Gabai

Seconded: Martin Bridson, Walter Neumann

Authors

D Cooper
Department of Mathematics University of California Santa Barbara CA 93106 USA

D D Long
Department of Mathematics University of California Santa Barbara CA 93106 USA

A W Reid
Department of Mathematics University of Texas Austin TX 78712 USA

Volume 11, issue 4 (2007)