Reducible and toroidal Dehn filling with distance 3

Description

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. / text

Links & Downloads

1. http://hdl.handle.net/2152/6682

Tags

Reducible Dehn filling

Toroidal Dehn filling

Distance 3

Whitehead link

Hyperbolic manifolds

Tangle arguments

Additional Fields

Identifer	oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/6682
Date	05 November 2009
Creators	Kang, Sungmo
Source Sets	University of Texas
Language	English
Detected Language	English
Format	electronic
Rights	Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.