Thickness of skeletons of arithmetic hyperbolic orbifolds

Abstract

We show that closed arithmetic hyperbolic [Formula: see text]-dimensional orbifolds with larger and larger volumes give rise to triangulations of the underlying spaces whose [Formula: see text]-skeletons are harder and harder to embed nicely in Euclidean space. To show this we generalize an inequality of Gromov and Guth to hyperbolic [Formula: see text]-orbifolds and find nearly optimal geodesic triangulations of arithmetic hyperbolic [Formula: see text]-orbifolds.