#### Volume 11, issue 4 (2007)

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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
##### 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
Primary: 57M10