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Rank gradient in co-final towers of certain Kleinian groupsGirão, Darlan Rabelo 01 February 2012 (has links)
This dissertation provides the first known examples of finite co-volume Kleinian groups which have co- final towers of finite index subgroups with positive
rank gradient. We prove that if the fundamental group of an orientable finite volume hyperbolic 3-manifold has fi nite index in the reflection group of a
right-angled ideal polyhedron in H^3 then it has a co-fi nal tower of fi nite sheeted covers with positive rank gradient. The manifolds we provide are also known
to have co- final towers of covers with zero rank gradient. We also prove that the reflection groups of compact right-angled hyperbolic polyhedra satisfying mild conditions have co-fi nal towers of fi nite sheeted covers with positive rank gradient. / text
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