{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/105626"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/105626","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Least dilatation of pure surface braids","abstract":"\"This thesis finds its roots in the Nielsen-Thurston classification of the mapping class group, a result that is fundamental to the field of low dimensional topology. In particular, Thurston's work gives us a powerful normal form for mapping classes: up to taking powers and restricting to subsurfaces, every mapping class can be decomposed into pieces which are either the identity or pseudo-Anosov. Associated to each of these pseudo-Anosov mapping classes is a unique algebraic number called its dilatation or ``stretch-factor\"\". In this thesis, we build on work of Penner who introduced the study of the minimal dilatation of pseudo-Anosovs in subgroups of the mapping class group. We prove upper and lower bounds on the minimal dilatation of pseudo-Anosovs in the $n$-stranded pure surface braid group extending results of Aougab--Taylor and Dowdall for the 1-stranded pure surface braid group.\"","abstract_html":""This thesis finds its roots in the Nielsen-Thurston classification of the mapping class group, a result that is fundamental to the field of low dimensional topology. In particular, Thurston's work gives us a powerful normal form for mapping classes: up to taking powers and restricting to subsurfaces, every mapping class can be decomposed into pieces which are either the identity or pseudo-Anosov. Associated to each of these pseudo-Anosov mapping classes is a unique algebraic number called its dilatation or ``stretch-factor"". In this thesis, we build on work of Penner who introduced the study of the minimal dilatation of pseudo-Anosovs in subgroups of the mapping class group. We prove upper and lower bounds on the minimal dilatation of pseudo-Anosovs in the $n$-stranded pure surface braid group extending results of Aougab--Taylor and Dowdall for the 1-stranded pure surface braid group."","abstract_has_math":true,"creators":["Loving, Marissa Kawehi"],"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","Dunfield, Nathan","Kapovich, Ilya","Kent, Autumn"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11-26T20:33:45Z","date_published":"2019-11-26T20:33:45Z","updated_at":"2026-07-22T22:24:44Z","subjects":["mapping class groups, pure surface braids, least dilatation, pseudo-Anosov"],"languages":["en"],"rights":["Copyright 2019 Marissa Kawehi Loving"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/105626","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leininger, Christopher","Dunfield, Nathan","Kapovich, Ilya","Kent, Autumn"]},{"key":"dc:creator","label":"Author","values":["Loving, Marissa Kawehi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-11-26T20:33:45Z","2019-07-02","2019-08"]},{"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":["mapping class groups, pure surface braids, least dilatation, pseudo-Anosov"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Marissa Kawehi Loving"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/105626"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"This thesis finds its roots in the Nielsen-Thurston classification of the mapping class group, a result that is fundamental to the field of low dimensional topology. In particular, Thurston's work gives us a powerful normal form for mapping classes: up to taking powers and restricting to subsurfaces, every mapping class can be decomposed into pieces which are either the identity or pseudo-Anosov. Associated to each of these pseudo-Anosov mapping classes is a unique algebraic number called its dilatation or ``stretch-factor\"\". In this thesis, we build on work of Penner who introduced the study of the minimal dilatation of pseudo-Anosovs in subgroups of the mapping class group. We prove upper and lower bounds on the minimal dilatation of pseudo-Anosovs in the $n$-stranded pure surface braid group extending results of Aougab--Taylor and Dowdall for the 1-stranded pure surface braid group.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-11-26 without embargo terms","The student, Marissa Loving, accepted the attached license on 2019-06-28 at 15:46.","The student, Marissa Loving, submitted this Dissertation for approval on 2019-06-28 at 18:09.","This Dissertation was approved for publication on 2019-07-02 at 17:21.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14110 on 2019-11-26 at 12:50:18","Made available in DSpace on 2019-11-26T20:33:45Z (GMT). No. of bitstreams: 3 LOVING-DISSERTATION-2019.pdf: 354278 bytes, checksum: 6f69d85f102503ee0755505292632b4c (MD5) Thesis - Marissa Loving (1).zip: 318511 bytes, checksum: 3f9bdf7d09f7e6937c05857cf0e96b31 (MD5) LICENSE.txt: 4211 bytes, checksum: 6790f517d20068e7b31028286ad812c6 (MD5) Previous issue date: 2019-07-02"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Least dilatation of pure surface braids"]}]}],"canonical_facts":{"dc:contributor":["Leininger, Christopher","Dunfield, Nathan","Kapovich, Ilya","Kent, Autumn"],"dc:creator":["Loving, Marissa Kawehi"],"dc:date":["2019-11-26T20:33:45Z","2019-07-02","2019-08"],"dc:description":["\"This thesis finds its roots in the Nielsen-Thurston classification of the mapping class group, a result that is fundamental to the field of low dimensional topology. In particular, Thurston's work gives us a powerful normal form for mapping classes: up to taking powers and restricting to subsurfaces, every mapping class can be decomposed into pieces which are either the identity or pseudo-Anosov. Associated to each of these pseudo-Anosov mapping classes is a unique algebraic number called its dilatation or ``stretch-factor\"\". In this thesis, we build on work of Penner who introduced the study of the minimal dilatation of pseudo-Anosovs in subgroups of the mapping class group. We prove upper and lower bounds on the minimal dilatation of pseudo-Anosovs in the $n$-stranded pure surface braid group extending results of Aougab--Taylor and Dowdall for the 1-stranded pure surface braid group.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-11-26 without embargo terms","The student, Marissa Loving, accepted the attached license on 2019-06-28 at 15:46.","The student, Marissa Loving, submitted this Dissertation for approval on 2019-06-28 at 18:09.","This Dissertation was approved for publication on 2019-07-02 at 17:21.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14110 on 2019-11-26 at 12:50:18","Made available in DSpace on 2019-11-26T20:33:45Z (GMT). No. of bitstreams: 3 LOVING-DISSERTATION-2019.pdf: 354278 bytes, checksum: 6f69d85f102503ee0755505292632b4c (MD5) Thesis - Marissa Loving (1).zip: 318511 bytes, checksum: 3f9bdf7d09f7e6937c05857cf0e96b31 (MD5) LICENSE.txt: 4211 bytes, checksum: 6790f517d20068e7b31028286ad812c6 (MD5) Previous issue date: 2019-07-02"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/105626"],"dc:language":["en"],"dc:rights":["Copyright 2019 Marissa Kawehi Loving"],"dc:subject":["mapping class groups, pure surface braids, least dilatation, pseudo-Anosov"],"dc:title":["Least dilatation of pure surface braids"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:44Z"}