{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/357537"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/357537","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Cubical small-cancellation theory and large-dimensional hyperbolic groups","abstract":"Given a finitely presented group Q and a compact special cube complex X with nonelementary hyperbolic fundamental group, we produce a non-elementary, torsion-free, cocompactly cubulated hyperbolic group Γ that surjects onto Q, with kernel isomorphic to a quotient of G = π_1X and such that max{cd(G),2} ≥ cd(Γ) ≥ cd(G)−1. Separately, we show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a C(9) cubical presentation is trivial, and use this to provide classifying spaces for proper actions for the fundamental groups of many quotients of square complexes admitting such cubical presentations. When the cubical presentations satisfy a condition analogous to requiring that the relators in a group presentation are not proper powers, we conclude that the corresponding coned-off space is aspherical.","abstract_html":"Given a finitely presented group Q and a compact special cube complex X with nonelementary hyperbolic fundamental group, we produce a non-elementary, torsion-free, cocompactly cubulated hyperbolic group Γ that surjects onto Q, with kernel isomorphic to a quotient of G = π_1X and such that max{cd(G),2} ≥ cd(Γ) ≥ cd(G)−1. Separately, we show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a C(9) cubical presentation is trivial, and use this to provide classifying spaces for proper actions for the fundamental groups of many quotients of square complexes admitting such cubical presentations. When the cubical presentations satisfy a condition analogous to requiring that the relators in a group presentation are not proper powers, we conclude that the corresponding coned-off space is aspherical.","abstract_has_math":false,"creators":["Arenas, Macarena"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Wilton, Henry"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-05-15","date_published":"2023-05-15","updated_at":"2026-07-22T22:24:32Z","subjects":["hyperbolic groups","cube complexes","small-cancellation theory"],"languages":["eng"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/1915c927-9913-48ee-a6af-b0b15e6f08b3/download","https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000349658121"],"render_values":[{"text":"0000-0003-4965-8121","href":"https://orcid.org/0000-0003-4965-8121","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.101703","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Wilton, Henry"]},{"key":"dc:contributor.sponsor","label":"Sponsor","values":["Cambridge Trust & Newnham College scholarship"]},{"key":"dc:creator","label":"Author","values":["Arenas, Macarena"]},{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000349658121"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2023-05-15"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/357537"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["hyperbolic groups","cube complexes","small-cancellation theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/1915c927-9913-48ee-a6af-b0b15e6f08b3/download","https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.101703"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/f6a15b5c-4dcb-4644-8070-3e579384a658/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Given a finitely presented group Q and a compact special cube complex X with nonelementary hyperbolic fundamental group, we produce a non-elementary, torsion-free, cocompactly cubulated hyperbolic group Γ that surjects onto Q, with kernel isomorphic to a quotient of G = π_1X and such that max{cd(G),2} ≥ cd(Γ) ≥ cd(G)−1. Separately, we show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a C(9) cubical presentation is trivial, and use this to provide classifying spaces for proper actions for the fundamental groups of many quotients of square complexes admitting such cubical presentations. When the cubical presentations satisfy a condition analogous to requiring that the relators in a group presentation are not proper powers, we conclude that the corresponding coned-off space is aspherical."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["0705a1a26770f70ca7b60e48c53c4764","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["Cubical small-cancellation theory and large-dimensional hyperbolic groups"]}]}],"canonical_facts":{"dc:contributor.advisor":["Wilton, Henry"],"dc:contributor.sponsor":["Cambridge Trust & Newnham College scholarship"],"dc:creator":["Arenas, Macarena"],"dc:creator.authoridentifier":["0000000349658121"],"dc:date.issued":["2023-05-15"],"dc:description.abstract":["Given a finitely presented group Q and a compact special cube complex X with nonelementary hyperbolic fundamental group, we produce a non-elementary, torsion-free, cocompactly cubulated hyperbolic group Γ that surjects onto Q, with kernel isomorphic to a quotient of G = π_1X and such that max{cd(G),2} ≥ cd(Γ) ≥ cd(G)−1. Separately, we show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a C(9) cubical presentation is trivial, and use this to provide classifying spaces for proper actions for the fundamental groups of many quotients of square complexes admitting such cubical presentations. When the cubical presentations satisfy a condition analogous to requiring that the relators in a group presentation are not proper powers, we conclude that the corresponding coned-off space is aspherical."],"dc:format.checksum.md5":["0705a1a26770f70ca7b60e48c53c4764","87eda9de84448d1f82354d60eee3eb5f"],"dc:identifier.doi":["https://doi.org/10.17863/CAM.101703"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/f6a15b5c-4dcb-4644-8070-3e579384a658/download"],"dc:language":["eng"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/357537"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/1915c927-9913-48ee-a6af-b0b15e6f08b3/download","https://creativecommons.org/licenses/by/4.0/"],"dc:subject":["hyperbolic groups","cube complexes","small-cancellation theory"],"dc:title":["Cubical small-cancellation theory and large-dimensional hyperbolic groups"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:24:32Z"}