Injectivity radii of hyperbolic integer homology 3-spheres

  title={Injectivity radii of hyperbolic integer homology 3-spheres},
  author={J. Brock and N. Dunfield},
  journal={Geometry & Topology},
  • J. Brock, N. Dunfield
  • Published 2015
  • Mathematics
  • Geometry & Topology
  • 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 which Benjamini-Schramm converge to H^3 whose normalized Ray-Singer analytic torsions do not converge to the L^2-analytic torsion of H^3. This contrasts with the work of Abert et. al. who showed that Benjamini-Schramm convergence forces convergence of normalized betti numbers. Our… CONTINUE READING
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