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Mathematics 2017, 5(3), 43;

On Minimal Covolume Hyperbolic Lattices

Department of Mathematics, University of Fribourg, CH-1700 Fribourg, Switzerland
Received: 10 July 2017 / Revised: 14 August 2017 / Accepted: 15 August 2017 / Published: 22 August 2017
(This article belongs to the Special Issue Geometry of Numbers)
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We study lattices with a non-compact fundamental domain of small volume in hyperbolic space H n . First, we identify the arithmetic lattices in Isom + H n of minimal covolume for even n up to 18. Then, we discuss the related problem in higher odd dimensions and provide solutions for n = 11 and n = 13 in terms of the rotation subgroup of certain Coxeter pyramid groups found by Tumarkin. The results depend on the work of Belolipetsky and Emery, as well as on the Euler characteristic computation for hyperbolic Coxeter polyhedra with few facets by means of the program CoxIter developed by Guglielmetti. This work complements the survey about hyperbolic orbifolds of minimal volume. View Full-Text
Keywords: hyperbolic lattice; cusp; minimal volume; arithmetic group; Coxeter polyhedron hyperbolic lattice; cusp; minimal volume; arithmetic group; Coxeter polyhedron

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Kellerhals, R. On Minimal Covolume Hyperbolic Lattices. Mathematics 2017, 5, 43.

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