Pro-p groups and towers of rational homology spheres

Nigel Boston; Jordan S Ellenberg

doi:10.2140/gt.2006.10.331

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arXiv · 0902.4567

Pro-p groups and towers of rational homology spheres

Nigel Boston·Jordan S Ellenberg

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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.

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Nigel Boston, Jordan S Ellenberg. 2009-02-26. Pro-p groups and towers of rational homology spheres. https://doi.org/10.2140/gt.2006.10.331

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