Browsing by Subject "Hyperbolic manifolds"
Now showing 1 - 2 of 2
- Results Per Page
- Sort Options
Item Rank gradient in co-final towers of certain Kleinian groups(2011-12) Girão, Darlan Rabelo; Reid, Alan W.; Gordon, Cameron; Luecke, John; Namazi, Hossein; Bajaj, ChandrajitThis 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.Item Reducible and toroidal Dehn filling with distance 3(2009-08) Kang, Sungmo; Gordon, Cameron, 1945-This dissertation is an investigation into the classification of all hyperbolic manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3. The first example was given by Boyer and Zhang. They used the Whitehead link. Eudave-Muñoz and Wu gave an infinite family of such hyperbolic manifolds using tangle arguments. I show in this dissertation that these are the only hyperbolic manifolds admitting a reducible Dehn filling and a toroidal Dehn filling with distance 3. The main tool to prove this is to use the intersection graphs on surfaces introduced and developed by Gordon and Luecke.