#### 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