Rank gradient in co-final towers of certain Kleinian groups

• Main Author: Girão, Darlan Rabelo
• Format: Others
• Language: English
• Published: 2012
• Subjects: Hyperbolic manifolds; Rank of fundamental groups; Right-angled polyhedra
• Online Access: http://hdl.handle.net/2152/ETD-UT-2011-12-4673

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