## Geometry & Topology

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

#### 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.

#### Article information

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

Dates
Accepted: 5 September 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799982

Digital Object Identifier
doi:10.2140/gt.2007.11.2265

Mathematical Reviews number (MathSciNet)
MR2372848

Zentralblatt MATH identifier
1140.57002

Subjects
Primary: 57M10: Covering spaces

#### Citation

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. https://projecteuclid.org/euclid.gt/1513799982

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