Injectivity radii of hyperbolic integer homology 3–spheres

Jeffrey F. Brock, Nathan M. Dunfield

Research output: Contribution to journalArticlepeer-review


We construct hyperbolic integer homology 3–spheres where the injectivity radius is arbitrarily large for nearly all points of the manifold. As a consequence, there exists a sequence of closed hyperbolic 3–manifolds that Benjamini–Schramm converge to ℍ3 whose normalized Ray–Singer analytic torsions do not converge to the L2 –analytic torsion of ℍ3. This contrasts with the work of Abert et al who showed that Benjamini– Schramm convergence forces convergence of normalized Betti numbers. Our results shed light on a conjecture of Bergeron and Venkatesh on the growth of torsion in the homology of arithmetic hyperbolic 3–manifolds, and we give experimental results which support this and related conjectures.

Original languageEnglish (US)
Pages (from-to)497-523
Number of pages27
JournalGeometry and Topology
Issue number1
StatePublished - Feb 27 2015

ASJC Scopus subject areas

  • Geometry and Topology


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