On volumes of quasi-arithmetic hyperbolic lattices

Abstract

We prove that the covolume of any quasi-arithmetic hyperbolic lattice (a notion that generalizes the definition of arithmetic subgroups) is a rational multiple of the covolume of an arithmetic subgroup. As a corollary, we obtain a good description for the shape of the volumes of most of the known hyperbolic n-manifolds with n>3.

11 pages. Final version. To appear in Selecta math

References in corpus (2)

• Quasi-arithmeticity of lattices in PO(n,1)
• A Classification of Non-Compact Coxeter Polytopes with $n+3$ Facets and One Non-Simple Vertex

Cited by in corpus (1)

• On faces of quasi-arithmetic Coxeter polytopes