Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Injectivity radii of hyperbolic integer homology 3-spheres   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 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.

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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat