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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