Non-coherence of arithmetic hyperbolic lattices

Abstract

We prove, under the assumption of the virtual fibration conjecture for arithmetic hyperbolic 3-manifolds, that all arithmetic lattices in O(n,1), n> 4, and different from 7, are non-coherent. We also establish noncoherence of uniform arithmetic lattices of the simplest type in SU(n,1), n> 1, and of uniform lattices in SU(2,1) which have infinite abelianization.

26 pages, 3 figures

References in corpus (2)

• Criteria for virtual fibering
• Noncoherence of some lattices in Isom(Hn)

Cited by in corpus (6)

• Virtually Fibering Right-Angled Coxeter Groups
• Virtual algebraic fibrations of Kähler groups
• Mapping class groups, multiple Kodaira fibrations, and CAT(0) spaces
• Hybrid lattices and thin subgroups of Picard modular groups
• NonLERFness of arithmetic hyperbolic manifold groups and mixed 3-manifold groups
• Special cubulation of strict hyperbolization