{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/79914"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/79914","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"Beyond Hyperbolicity: Generalizing Classical Results from Hyperbolic Groups to all Finitely Generated Groups","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Zalloum, Abdalrazzaq"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Mangahas, Johanna","Mathematics"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-07-30T15:11:04Z","date_published":"2019-07-30T15:11:04Z","updated_at":"2026-07-27T19:05:21Z","subjects":["mathematics"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/79914","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mangahas, Johanna","Mathematics"]},{"key":"dc:creator","label":"Author","values":["Zalloum, Abdalrazzaq"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-07-30T15:11:04Z","2019","2019-05-11 06:15:56"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/79914"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","Let X be a proper geodesic metric space. We give a new construction of the Morse Boundary that realizes its points as equivalence classes of functions on X which behave similar to the “distance to a point\" function. When G = hS i is a finitely generated group and X = Cay(G, S), we use this construction to give a sym-bolic presentation of the Morse boundary as a space of “derivatives\" on Cay(G, S). For a proper complete CAT(0) space, we show that horospheres corresponding to Morse points behave similar to horospheres in the hyperbolic space H^n . Let G be a finitely generated group. We show that for any generating set A, the language consisting of all geodesics in Cay(G, A) with a contracting property is a regular language. As an application, we show that any finitely generated group containing an infinite contracting geodesic must be either virtually Z or acylindrically hyperbolic."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Beyond Hyperbolicity: Generalizing Classical Results from Hyperbolic Groups to all Finitely Generated Groups"]}]}],"canonical_facts":{"dc:contributor":["Mangahas, Johanna","Mathematics"],"dc:creator":["Zalloum, Abdalrazzaq"],"dc:date":["2019-07-30T15:11:04Z","2019","2019-05-11 06:15:56"],"dc:description":["Ph.D.","Let X be a proper geodesic metric space. We give a new construction of the Morse Boundary that realizes its points as equivalence classes of functions on X which behave similar to the “distance to a point\" function. When G = hS i is a finitely generated group and X = Cay(G, S), we use this construction to give a sym-bolic presentation of the Morse boundary as a space of “derivatives\" on Cay(G, S). For a proper complete CAT(0) space, we show that horospheres corresponding to Morse points behave similar to horospheres in the hyperbolic space H^n . Let G be a finitely generated group. We show that for any generating set A, the language consisting of all geodesics in Cay(G, A) with a contracting property is a regular language. As an application, we show that any finitely generated group containing an infinite contracting geodesic must be either virtually Z or acylindrically hyperbolic."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/79914"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["mathematics"],"dc:title":["Beyond Hyperbolicity: Generalizing Classical Results from Hyperbolic Groups to all Finitely Generated Groups"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:21Z"}