{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/45424"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/45424","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Hyperbolic 3-manifolds of bounded volume and trace field degree","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Jeon, Bo Gwang"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Dunfield, Nathan M.","Leininger, Christopher J.","Ahlgren, Scott","Athreya, Jayadev S."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-08-22T16:39:45Z","date_published":"2013-08-22T16:39:45Z","updated_at":"2026-07-22T22:25:34Z","subjects":["Hyperbolic 3-Manifolds","Volume","Dehn Filling","Trace Field"],"languages":["en"],"rights":["Copyright 2013 Bo Gwang Jeon"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/45424","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dunfield, Nathan M.","Leininger, Christopher J.","Ahlgren, Scott","Athreya, Jayadev S."]},{"key":"dc:creator","label":"Author","values":["Jeon, Bo Gwang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-08-22T16:39:45Z","2013-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Hyperbolic 3-Manifolds","Volume","Dehn Filling","Trace Field"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2013 Bo Gwang Jeon"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/45424"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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). 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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). 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