From geometry to arithmetic of compact hyperbolic Coxeter polytopes

Abstract

We establish some geometric constraints on compact Coxeter polytopes in hyperbolic spaces and show that these constraints can be a very useful tool for the classification problem of reflective anisotropic Lorentzian lattices and cocompact arithmetic hyperbolic reflection groups.

arXiv comment27 pages, 2 figures, 4 tables; substantial revision of the introduction