Groups, Geometry, and Dynamics


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Volume 8, Issue 1, 2014, pp. 143–155
DOI: 10.4171/GGD/220

Published online: 2014-05-13

Rank gradient in co-final towers of certain Kleinian groups

Darlan Girão[1]

(1) Universidade Federal do Ceará, Fortaleza, Brazil

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.

Keywords: Kleinian groups, rank of groups

Girão Darlan: Rank gradient in co-final towers of certain Kleinian groups. Groups Geom. Dyn. 8 (2014), 143-155. doi: 10.4171/GGD/220