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Pro–p groups and towers of rational homology spheres
Nigel Boston and Jordan S Ellenberg
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Geometry & Topology 10 (2006)
331–334
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Abstract
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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.
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Keywords
pro–p group, hyperbolic
3–manifold, rational homology sphere
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Mathematical Subject Classification
Primary: 20E18
Secondary: 22E40
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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
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