Hyperbolic 3-manifolds of bounded volume and trace field degree

Jeon, Bo Gwang

Permalink

https://hdl.handle.net/2142/45424 Copy

Description

Title

Hyperbolic 3-manifolds of bounded volume and trace field degree

Author(s)

Jeon, Bo Gwang

Issue Date

2013-08-22T16:39:45Z

Director of Research (if dissertation) or Advisor (if thesis)

Dunfield, Nathan M.

Doctoral Committee Chair(s)

Leininger, Christopher J.

Committee Member(s)

• Dunfield, Nathan M.
• Ahlgren, Scott
• Athreya, Jayadev S.

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

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

Abstract

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.

Graduation Semester

2013-08

Permalink

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

Copyright and License Information

Copyright 2013 Bo Gwang Jeon

Owning Collections