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Title:Hyperbolic 3-manifolds of bounded volume and trace field degree
Author(s):Jeon, Bo Gwang
Director of Research:Dunfield, Nathan M.
Doctoral Committee Chair(s):Leininger, Christopher J.
Doctoral Committee Member(s):Dunfield, Nathan M.; Ahlgren, Scott; Athreya, Jayadev S.
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Hyperbolic 3-Manifolds
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.
Issue Date:2013-08-22
Rights Information:Copyright 2013 Bo Gwang Jeon
Date Available in IDEALS:2013-08-22
Date Deposited:2013-08

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