Rank gradient in co-final towers of certain Kleinian groups

Abstract

We prove that if the fundamental group of an orientable finite volume hyperbolic 3-manifold has finite index in the reflection group of a right-angled ideal polyhedron in ${\mathbb{H}}^3$ then it has a co-final tower of finite sheeted covers with positive rank gradient. The manifolds we consider are also known to have co-final towers of covers with zero rank gradient.