On Minimal Covolume Hyperbolic Lattices

Mathematics

Ruth Kellerhals¹ 

[1] Department of Mathematics, University of Fribourg, CH-1700 Fribourg, Switzerland;

关键词: hyperbolic lattice;    cusp;    minimal volume;    arithmetic group;    Coxeter polyhedron;   

DOI  :  10.3390/math5030043

来源: DOAJ

【 摘 要 】

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 nof 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.

【 授权许可】

Unknown