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Dunfield, Nathan M. Leininger, Christopher J. Dunfield, Nathan M. Ahlgren, Scott Athreya, Jayadev S. Jeon, Bo Gwang 2013-08-22T16:39:45Z 2013-08-22T16:39:45Z 2013-08 2013-08-22T16:39:45Z 2013-08 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-06-24T13:33:38Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 BoGwang_Jeon.pdf: 367899 bytes, checksum: 85d5c2afbd6b6a13881cf4cb79c56ec9 (MD5) Made available in DSpace on 2013-08-22T16:39:45Z (GMT). No. of bitstreams: 2 Bo Gwang_Jeon.pdf: 367899 bytes, checksum: 85d5c2afbd6b6a13881cf4cb79c56ec9 (MD5) license.txt: 4061 bytes, checksum: 36f07266d310e14a9b659c62f8132632 (MD5) http://hdl.handle.net/2142/45424 en Copyright 2013 Bo Gwang Jeon Hyperbolic 3-Manifolds Volume Dehn Filling Trace Field Hyperbolic 3-manifolds of bounded volume and trace field degree text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD