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On the virtual Betti numbers of arithmetic hyperbolic 3–manifolds

Daryl Cooper, Darren Long and Alan 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

Primary: 57M10
References
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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
Daryl Cooper
Department of Mathematics
University of California
Santa Barbara CA 93106
USA
Darren Long
Department of Mathematics
University of California
Santa Barbara CA 93106
USA
Alan W Reid
Department of Mathematics
University of Texas
Austin TX 78712
USA