#### Volume 10, issue 1 (2006)

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Pro–$p$ groups and towers of rational homology spheres

### Nigel Boston and Jordan S Ellenberg

Geometry & Topology 10 (2006) 331–334
 arXiv: 0902.4567
##### Abstract

In the preceding paper, Calegari and Dunfield exhibit a sequence of hyperbolic 3–manifolds which have increasing injectivity radius, and which, subject to some conjectures in number theory, are rational homology spheres. We prove unconditionally that these manifolds are rational homology spheres, and give a sufficient condition for a tower of hyperbolic 3–manifolds to have first Betti number 0 at each level. The methods involved are purely pro–p group theoretical.

##### Keywords
pro–$p$ group, hyperbolic 3–manifold, rational homology sphere
Primary: 20E18
Secondary: 22E40
##### Publication
Revised: 11 December 2005
Accepted: 2 January 2006
Published: 2 April 2006
Proposed: Walter Neumann
Seconded: David Gabai, Tomasz Mrowka
##### Authors
 Nigel Boston Department of Mathematics University of Wisconsin Van Vleck Hall 480 Lincoln Drive Madison WI 53706 USA Jordan S Ellenberg Department of Mathematics University of Wisconsin Van Vleck Hall 480 Lincoln Drive Madison WI 53706 USA