Rank gradient in co-final towers of certain Kleinian groups
| dc.contributor.advisor | Reid, Alan W. | en |
| dc.contributor.committeeMember | Gordon, Cameron | en |
| dc.contributor.committeeMember | Luecke, John | en |
| dc.contributor.committeeMember | Namazi, Hossein | en |
| dc.contributor.committeeMember | Bajaj, Chandrajit | en |
| dc.creator | Girão, Darlan Rabelo | en |
| dc.date.accessioned | 2012-02-01T20:06:50Z | en |
| dc.date.available | 2012-02-01T20:06:50Z | en |
| dc.date.issued | 2011-12 | en |
| dc.date.submitted | December 2011 | en |
| dc.date.updated | 2012-02-01T20:06:59Z | en |
| dc.description | text | en |
| dc.description.abstract | 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. | en |
| dc.description.department | Mathematics | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.slug | 2152/ETD-UT-2011-12-4673 | en |
| dc.identifier.uri | http://hdl.handle.net/2152/ETD-UT-2011-12-4673 | en |
| dc.language.iso | eng | en |
| dc.subject | Hyperbolic manifolds | en |
| dc.subject | Rank of fundamental groups | en |
| dc.subject | Right-angled polyhedra | en |
| dc.title | Rank gradient in co-final towers of certain Kleinian groups | en |
| dc.type.genre | thesis | en |
| thesis.degree.department | Mathematics | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | University of Texas at Austin | en |
| thesis.degree.level | Doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |