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Integral Congruence Two Hyperbolic 5-Manifolds

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Abstract

In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H 5/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ 5 2 of the group Γ 5 of positive units of the Lorentzian quadratic form x 2/1 +... +x 5/2 -x 6/2. We also show that Γ 5 2 is a reflection group with respect to a 5-dimensional right-angled convex polytope in H 5. As an application, we construct a hyperbolic 5-manifold of smallest known volume 7ζ (3)/4.

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Authors and Affiliations

  1. Department of Mathematics, Vanderbilt University, Nashville, TN 37240, U.S.A.

    John G. Ratcliffe & Steven T. Tschantz

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  1. John G. Ratcliffe
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  2. Steven T. Tschantz
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Ratcliffe, J.G., Tschantz, S.T. Integral Congruence Two Hyperbolic 5-Manifolds. Geometriae Dedicata 107, 187–209 (2004). https://doi.org/10.1007/s10711-004-8120-y

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