{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/113005"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/113005","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Free products of abelian groups in mapping class groups","abstract":"The notions of convex cocompactness and geometric finiteness originally come from the study of Kleinian groups. The analogous notion of convex cocompactness for mapping class groups is due to Farb-Mosher. In recent work, Dowdall-Durham-Leininger-Sisto have proposed a definition of “parabolic” geometric finiteness for mapping class groups. In this thesis, we construct a new family of examples of parabolically geometrically finite mapping class subgroups and prove that they are undistorted in Mod(S). We also prove that a subfamily of our examples are also geometrically finite in the sense of Durham-Hagen-Sisto.","abstract_html":"The notions of convex cocompactness and geometric finiteness originally come from the study of Kleinian groups. The analogous notion of convex cocompactness for mapping class groups is due to Farb-Mosher. In recent work, Dowdall-Durham-Leininger-Sisto have proposed a definition of “parabolic” geometric finiteness for mapping class groups. In this thesis, we construct a new family of examples of parabolically geometrically finite mapping class subgroups and prove that they are undistorted in Mod(S). We also prove that a subfamily of our examples are also geometrically finite in the sense of Durham-Hagen-Sisto.","abstract_has_math":false,"creators":["Loa, Christopher"],"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","Dunfield, Nathan","Bradlow, Steven","Sadanand, Chandrika"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-01-12T21:45:31Z","date_published":"2022-01-12T21:45:31Z","updated_at":"2026-07-22T22:24:52Z","subjects":["geometry","topology"],"languages":["en"],"rights":["Copyright 2021 Christopher Loa"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/113005","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leininger, Christopher J","Dunfield, Nathan","Bradlow, Steven","Sadanand, Chandrika"]},{"key":"dc:creator","label":"Author","values":["Loa, Christopher"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-01-12T21:45:31Z","2021-07-13","2021-08"]},{"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":["geometry","topology"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2021 Christopher Loa"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/113005"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The notions of convex cocompactness and geometric finiteness originally come from the study of Kleinian groups. 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