The cusped hyperbolic orbifolds of minimal volume in dimensions less than ten

DOI10.1016/j.jalgebra.2006.12.024zbMath1119.52011OpenAlexW2067829681MaRDI QIDQ2370303

Thierry Hild

Publication date: 25 June 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.12.024

zbMATH Keywords

volumehoroball packingcrystallographic groupcusped hyperbolic orbifold

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) General geometric structures on low-dimensional manifolds (57M50) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items (max. 100)

Hyperbolic Coxeter groups of minimal growth rates in higher dimensions ⋮ On volumes of hyperbolic Coxeter polytopes and quadratic forms ⋮ The densest lattices in \(\mathrm{PGL}_3(\mathbb Q_2)\) ⋮ On minimal covolume hyperbolic lattices ⋮ The non-arithmetic cusped hyperbolic 3-orbifold of minimal volume ⋮ Small‐volume hyperbolic manifolds constructed from Coxeter groups ⋮ Quaternionic hyperbolic lattices of minimal covolume ⋮ Scissors congruence, the golden ratio and volumes in hyperbolic 5-space ⋮ On volumes of hyperbolic orbifolds ⋮ On the number of ends of rank one locally symmetric spaces ⋮ Hyperbolic orbifolds of minimal volume ⋮ Spiraling spectra of geodesic lines in negatively curved manifolds ⋮ Hyperbolic Coxeter groups and minimal growth rates in dimensions four and five

Cites Work

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• Geometry II: spaces of constant curvature. Transl. from the Russian by V. Minachin
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• Volumes of cusped hyperbolic manifolds
• The size of hyperbolic Coxeter simplex
• Some remarks on discontinuous groups
• The cusped hyperbolic 3-orbifold of minimum volume
• Packing of spheres in spaces of constant curvature
• On maximal finite irreducible subgroups of 𝐺𝐿(𝑛,𝑍). V. The eight-dimensional case and a complete description of dimensions less than ten
• On Maximal Finite Irreducible Subgroups of GL(n, Z ): I. The Five and Seven Dimensional Cases
• On Maximal Finite Irreducible Subgroups of GL(n, Z ): II. The Six Dimensional Case
• The fcc lattice and the cusped hyperbolic 4-orbifold of minimal volume: In memoriam H. S. M. Coxeter

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