Integral Congruence Two Hyperbolic 5-Manifolds

2003/08/13 by John G. Ratcliffe, Ratcliffe, John G., Steven T. Tschantz +1
Mathematics · #30F40 #51M10 #53C25 #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DG #math.GT #msc:30F40 #msc:51M10 #msc:53C25

paper · pdf · doi:10.48550/arxiv.math/0308125

21 pages, 2 figures, LaTeX

arxiv created 2003/08/13 · openalex publication_date 2003/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H⁵/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ⁵₂ of the group Γ⁵ of positive units of the Lorentzian quadratic form x₁²+...+x₅²-x₆². We also show that Γ⁵₂ is a reflection group with respect to a 5-dimensional right-angled convex polytope in H⁵. As an application, we construct a hyperbolic 5-manifold of smallest known volume 7ζ(3)/4.

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