{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/108514"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/108514","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Low dilatation pseudo-anosovs on punctured surfaces and volume","abstract":"For a pseudo-Anosov homeomorphism f on a closed surface of genus g greater of equals to 2, for which the entropy is on the order 1/g (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded, independent of g. We show that the analogous result fails for a surface of fixed genus g with n punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order (log n)/n, and volume tending to infinity.","abstract_html":"For a pseudo-Anosov homeomorphism f on a closed surface of genus g greater of equals to 2, for which the entropy is on the order 1/g (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded, independent of g. We show that the analogous result fails for a surface of fixed genus g with n punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order (log n)/n, and volume tending to infinity.","abstract_has_math":false,"creators":["Li, Shixuan"],"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","Kapovich, Ilya","Dunfield, Nathan","Bradlow, Steven"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-10-07T21:00:03Z","date_published":"2020-10-07T21:00:03Z","updated_at":"2026-07-22T22:24:48Z","subjects":["pseudo-Anosovs","volume","punctured surfaces","mapping torus"],"languages":["en"],"rights":["Copyright 2020 by Shixuan Li. All rights reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/108514","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leininger, Christopher","Kapovich, Ilya","Dunfield, Nathan","Bradlow, Steven"]},{"key":"dc:creator","label":"Author","values":["Li, Shixuan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-10-07T21:00:03Z","2020-07-17","2020-08"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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":["pseudo-Anosovs","volume","punctured surfaces","mapping torus"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 by Shixuan Li. All rights reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/108514"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["For a pseudo-Anosov homeomorphism f on a closed surface of genus g greater of equals to 2, for which the entropy is on the order 1/g (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded, independent of g. We show that the analogous result fails for a surface of fixed genus g with n punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order (log n)/n, and volume tending to infinity.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms","The student, Shixuan Li, accepted the attached license on 2020-07-17 at 03:40.","The student, Shixuan Li, submitted this Dissertation for approval on 2020-07-17 at 03:58.","This Dissertation was approved for publication on 2020-07-17 at 17:07.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15671 on 2020-10-02 at 15:14:52","Made available in DSpace on 2020-10-07T21:00:03Z (GMT). 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We show that the analogous result fails for a surface of fixed genus g with n punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order (log n)/n, and volume tending to infinity.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms","The student, Shixuan Li, accepted the attached license on 2020-07-17 at 03:40.","The student, Shixuan Li, submitted this Dissertation for approval on 2020-07-17 at 03:58.","This Dissertation was approved for publication on 2020-07-17 at 17:07.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15671 on 2020-10-02 at 15:14:52","Made available in DSpace on 2020-10-07T21:00:03Z (GMT). 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