Volume 10, issue 1 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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
Mathematical Subject Classification 2000
Primary: 20E18
Secondary: 22E40
References
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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
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