{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/120373"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/120373","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stable subgroups of handlebody groups","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01","abstract_has_math":false,"creators":["Chesser, Marissa"],"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","Hirani, Anil","Sadanand, Chandrika"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-05","date_published":"2023-05","updated_at":"2026-07-22T22:24:57Z","subjects":["Geometric Group Theory","Handlebody Groups"],"languages":["en","eng"],"rights":["Copyright 2023 Marissa Chesser"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/120373","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leininger, Christopher","Dunfield, Nathan","Hirani, Anil","Sadanand, Chandrika"]},{"key":"dc:creator","label":"Author","values":["Chesser, Marissa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05","2023-04-16"]},{"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":["Geometric Group Theory","Handlebody Groups"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2023 Marissa Chesser"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/120373"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01","The student, Marissa Chesser, accepted the attached license on 2023-04-14 at 14:00.","The student, Marissa Chesser, submitted this Dissertation for approval on 2023-04-14 at 14:05.","This Dissertation was approved for publication on 2023-04-16 at 14:19.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18989 on 2023-09-01 at 17:13:31","The main result of this thesis is that a finitely generated subgroup of the genus two handlebody group is stable if and only if the orbit map to the disk graph is a quasi-isometric embedding. To this end, we prove that the genus two handlebody group is a hierarchically hyperbolic group, and that the maximal hyperbolic space in the hierarchy is quasi-isometric to the disk graph of a genus two handlebody by appealing to a construction of Hamenstadt-Hensel. We then utilize the characterization of stable subgroups of hierarchically hyperbolic groups provided by Abbott-Behrstock-Durham. We also present several applications of the main theorems, and show that the higher genus analogues of the genus two results do not hold."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Stable subgroups of handlebody groups"]}]}],"canonical_facts":{"dc:contributor":["Leininger, Christopher","Dunfield, Nathan","Hirani, Anil","Sadanand, Chandrika"],"dc:creator":["Chesser, Marissa"],"dc:date":["2023-05","2023-04-16"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01","The student, Marissa Chesser, accepted the attached license on 2023-04-14 at 14:00.","The student, Marissa Chesser, submitted this Dissertation for approval on 2023-04-14 at 14:05.","This Dissertation was approved for publication on 2023-04-16 at 14:19.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18989 on 2023-09-01 at 17:13:31","The main result of this thesis is that a finitely generated subgroup of the genus two handlebody group is stable if and only if the orbit map to the disk graph is a quasi-isometric embedding. To this end, we prove that the genus two handlebody group is a hierarchically hyperbolic group, and that the maximal hyperbolic space in the hierarchy is quasi-isometric to the disk graph of a genus two handlebody by appealing to a construction of Hamenstadt-Hensel. We then utilize the characterization of stable subgroups of hierarchically hyperbolic groups provided by Abbott-Behrstock-Durham. We also present several applications of the main theorems, and show that the higher genus analogues of the genus two results do not hold."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/120373"],"dc:language":["en","eng"],"dc:rights":["Copyright 2023 Marissa Chesser"],"dc:subject":["Geometric Group Theory","Handlebody Groups"],"dc:title":["Stable subgroups of handlebody groups"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:57Z"}