Abstract
We discuss the geometry of some arithmetic orbifolds locally isometric to a product X of real hyperbolic spaces ℍ m of dimension m=2,3, and prove that certain sequences of non-compact orbifolds are convergent to X in a geometric (“Benjamini–Schramm”) sense for low-dimensional cases (when X is equal to ℍ 2 ×ℍ 2 or ℍ 3 ). We also deal with 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.
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