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
We study lattices with a non-compact fundamental domain of small volume in hyperbolic space
. First, we identify the arithmetic lattices in
of minimal covolume for even n
up to 18. Then, we discuss the related problem in higher odd dimensions and provide solutions for
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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Kellerhals, R. On Minimal Covolume Hyperbolic Lattices. Mathematics 2017, 5, 43.
Kellerhals R. On Minimal Covolume Hyperbolic Lattices. Mathematics. 2017; 5(3):43.
Kellerhals, Ruth. 2017. "On Minimal Covolume Hyperbolic Lattices." Mathematics 5, no. 3: 43.
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