Geometry & Topology

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

Daryl Cooper, Darren Long, and Alan W Reid

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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.

Article information

Geom. Topol., Volume 11, Number 4 (2007), 2265-2276.

Received: 13 December 2006
Accepted: 5 September 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M10: Covering spaces

virtual Betti number large fundamental group


Cooper, Daryl; Long, Darren; Reid, Alan W. On the virtual Betti numbers of arithmetic hyperbolic $3$–manifolds. Geom. Topol. 11 (2007), no. 4, 2265--2276. doi:10.2140/gt.2007.11.2265.

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