Hyperbolic 3-manifolds of bounded volume and trace field degree

For a single cusped hyperbolic 3-manifold, Hodgson proved that there are only finitely many Dehn fillings of it whose trace fields have bounded degree. In this paper, we conjecture the same for manifolds with more cusps, and give the first positive results in this direction. For example, in the 2-cusped case, if a manifold has linearly independent cusp shapes, we show that the manifold has the desired property. To prove the results, we use Habegger's proof of the Bounded Height Conjecture in arithmetic geometry.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Jeon, Bo Gwang

Contributors dc:contributor

• Dunfield, Nathan M.
• Leininger, Christopher J.
• Ahlgren, Scott
• Athreya, Jayadev S.

• Hyperbolic 3-Manifolds
• Volume
• Dehn Filling
• Trace Field

Statement dc:rights

• Copyright 2013 Bo Gwang Jeon

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/45424

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/45424