Analytic torsion convergence conjecture for Benjamini–Schramm covers
Analytic torsion convergence conjecture for Benjamini–Schramm covers
Let be a fixed closed hyperbolic -manifold, and let be covers of that Benjamini–Schramm converge to hyperbolic -space . The analytic torsion convergence conjecture. One should have
This is presented as a broadening of the first, analytic-torsion part of the Bergeron–Venkatesh conjecture from arithmetic towers to all covers of a fixed closed hyperbolic -manifold. The source reports computational evidence supporting it, while also giving examples showing that Benjamini–Schramm convergence alone does not force the same conclusion for arbitrary sequences.
Sources & referencesView supporting material
Primary source
Jeffrey F. Brock and Nathan M. Dunfield, “Injectivity radii of hyperbolic integer homology 3-spheres”, arXiv:1304.0391 (2014).
Additional references
2 papers in this index state this conjecture (2012–2013). The statement above is taken from the most recent of them; the others are arXiv:1210.2961.
Progress summary
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