{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/104790"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/104790","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Boundaries and hierarchically hyperbolic spaces","abstract":"Although the hierarchically hyperbolic space boundary is a generalization of the Gromov boundary, we will show there are fundamental differences between the two. First, we provide negative answers to questions posed by Durham, Hagen, and Sisto on the existence of boundary maps for some hierarchically hyperbolic spaces, namely maps from right-angled Artin groups to mapping class groups. We then answer another question of Durham, Hagen, and Sisto, proving that a Teichmuller geodesic ray does not necessarily converge to a unique point in the hierarchically hyperbolic space boundary of Teichmuller space. In fact, we prove that the limit set can be almost anything allowed by the topology.","abstract_html":"Although the hierarchically hyperbolic space boundary is a generalization of the Gromov boundary, we will show there are fundamental differences between the two. First, we provide negative answers to questions posed by Durham, Hagen, and Sisto on the existence of boundary maps for some hierarchically hyperbolic spaces, namely maps from right-angled Artin groups to mapping class groups. We then answer another question of Durham, Hagen, and Sisto, proving that a Teichmuller geodesic ray does not necessarily converge to a unique point in the hierarchically hyperbolic space boundary of Teichmuller space. In fact, we prove that the limit set can be almost anything allowed by the topology.","abstract_has_math":false,"creators":["Mousley, Sarah C."],"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","Kapovich, Ilya","Schupp, Paul"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-08-23T19:51:43Z","date_published":"2019-08-23T19:51:43Z","updated_at":"2026-07-22T22:24:42Z","subjects":["Teichmuller space","mapping class group","right-angled Artin group","hierarchically hyperbolic","limit set"],"languages":["en"],"rights":["Copyright 2019 Sarah Camille Mousley Mackay"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/104790","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","Kapovich, Ilya","Schupp, Paul"]},{"key":"dc:creator","label":"Author","values":["Mousley, Sarah C."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-08-23T19:51:43Z","2019-04-10","2019-05"]},{"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":["Teichmuller space","mapping class group","right-angled Artin group","hierarchically hyperbolic","limit set"]}]},{"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 Sarah Camille Mousley Mackay"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/104790"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Although the hierarchically hyperbolic space boundary is a generalization of the Gromov boundary, we will show there are fundamental differences between the two. 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