Geometry & Topology 10 (2006) 331–334

DOI: 10.2140/gt.2006.10.331

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

Mathematical Subject Classification

Primary: 20E18

Secondary: 22E40

References

Publication

Received: 22 November 2005
Revised: 11 December 2005
Accepted: 2 January 2006
Published: 2 April 2006
Proposed: Walter Neumann
Seconded: David Gabai, Tomasz Mrowka

Authors