On the convergence of arithmetic orbifolds
Geometric Topology
2018-02-14 v2 Group Theory
Number Theory
Abstract
We discuss the geometry of some arithmetic orbifolds locally isometric to a product of real hyperbolic spaces of dimension two and three, and prove that certain sequences of non-uniform orbifolds are convergent to this space in a geometric ("Benjamini--Schramm") sense for hyperbolic three--space and a product of hyperbolic planes. We also deal with arbitrary sequences of maximal arithmetic three--dimensional hyperbolic lattices defined over a quadratic or cubic field. A motivating application is the study of Betti numbers of Bianchi groups.
Cite
@article{arxiv.1311.5375,
title = {On the convergence of arithmetic orbifolds},
author = {Jean Raimbault},
journal= {arXiv preprint arXiv:1311.5375},
year = {2018}
}
Comments
Final version, 51 pages (journal layout). Minor correction to the main theorem from the first version