{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/98133"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/98133","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Dynamics of free group automorphisms and a subgroup alternative for out(fn)","abstract":"This thesis is motivated by a foundational result of Thurston which states that pseudo- Anosov mapping classes act on the compactified Teichmüller space with north-south dynamics. We prove that several analogues of pseudo-Anosov mapping classes in the Out(F_N) setting act on the space of projective geodesic currents with generalized north-south dynamics. As an application of our results, we prove several structural theorems for subgroups of Out(F_N).","abstract_html":"This thesis is motivated by a foundational result of Thurston which states that pseudo- Anosov mapping classes act on the compactified Teichmüller space with north-south dynamics. We prove that several analogues of pseudo-Anosov mapping classes in the Out(F_N) setting act on the space of projective geodesic currents with generalized north-south dynamics. As an application of our results, we prove several structural theorems for subgroups of Out(F_N).","abstract_has_math":false,"creators":["Uyanik, Caglar"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Leininger, Christopher J.","Kapovich, Ilya","Tyson, Jeremy","Dunfield, Nathan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-09-29T16:38:03Z","date_published":"2017-09-29T16:38:03Z","updated_at":"2026-07-22T22:24:35Z","subjects":["Free groups","Mapping class groups","Pseudo-Anosov","Fully irreducible","Hyperbolic"],"languages":["en"],"rights":["Copyright 2017 Caglar Uyanik"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/98133","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leininger, Christopher J.","Kapovich, Ilya","Tyson, Jeremy","Dunfield, Nathan"]},{"key":"dc:creator","label":"Author","values":["Uyanik, Caglar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-09-29T16:38:03Z","2017-06-26","2017-08"]},{"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":["Free groups","Mapping class groups","Pseudo-Anosov","Fully irreducible","Hyperbolic"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Caglar Uyanik"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/98133"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis is motivated by a foundational result of Thurston which states that pseudo- Anosov mapping classes act on the compactified Teichmüller space with north-south dynamics. 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We prove that several analogues of pseudo-Anosov mapping classes in the Out(F_N) setting act on the space of projective geodesic currents with generalized north-south dynamics. As an application of our results, we prove several structural theorems for subgroups of Out(F_N).","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-09-29 without embargo terms","The student, Caglar Uyanik, accepted the attached license on 2017-06-26 at 13:10.","The student, Caglar Uyanik, submitted this Dissertation for approval on 2017-06-26 at 13:16.","This Dissertation was approved for publication on 2017-06-26 at 17:15.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11268 on 2017-09-29 at 11:27:13","Made available in DSpace on 2017-09-29T16:38:03Z (GMT). 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