{"id":{"repo_id":"unr","oai_identifier":"oai:scholarwolf.unr.edu:11714/11605"},"canonical_url":"https://search.dev.ndltd.org/etd/unr/oai:scholarwolf.unr.edu:11714/11605","repository":{"repo_id":"unr","name":"University of Nevada - Reno","base_url":"https://scholarwolf.unr.edu/server/oai/request"},"display":{"title":"Scalar Curvature Constraints on Symplectic 4-Manifolds","abstract":"This thesis presents a remarkable result, that showcases an unexpected interplaybetween Riemannian geometry and symplectic topology on 4-manifolds. These two branches of mathematics belong to different worlds: Where geometry concerns it- self with distances, angles, areas, curvatures, etc., all of which typically vary from one point on the manifold to the next, topology studies properties of manifolds that are unaltered and remain constant when varying the metric. 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In this thesis we first provide a general overview of spin geometry on Riemannian manifolds and then es- tablish a fundamental restriction on the scalar curvature induced by the topology of a symplectic manifold.","abstract_has_math":false,"creators":["Galloway, Brian"],"institution":null,"degree_name":null,"degree_level":"Master's Degree","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Jabuka, Stanislav"],"committee_chairs":[],"committee_members":["Herald, Christopher","Tavakkoli, Alireza"],"year":2025,"date_issued":"2025","date_published":"2025","updated_at":"2026-07-27T21:45:57Z","subjects":["Dirac operatior","scalar curvature","spin geometry","symplectic manifolds"],"languages":["en_US","English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarwolf.unr.edu/handle/11714/11605","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Jabuka, Stanislav"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Herald, Christopher","Tavakkoli, Alireza"]},{"key":"dc:creator","label":"Author","values":["Galloway, Brian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-09-08T18:49:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-09-08T18:49:13Z"]},{"key":"dc:date.issued","label":"Date","values":["2025"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's Degree"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Dirac operatior","scalar curvature","spin geometry","symplectic manifolds"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://scholarwolf.unr.edu/handle/11714/11605"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis presents a remarkable result, that showcases an unexpected interplaybetween Riemannian geometry and symplectic topology on 4-manifolds. 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In this thesis we first provide a general overview of spin geometry on Riemannian manifolds and then es- tablish a fundamental restriction on the scalar curvature induced by the topology of a symplectic manifold."]},{"key":"dc:format","label":"Dc Format","values":["PDF"]},{"key":"dc:title","label":"Title","values":["Scalar Curvature Constraints on Symplectic 4-Manifolds"]}]}],"canonical_facts":{"dc:contributor.advisor":["Jabuka, Stanislav"],"dc:contributor.committeemember":["Herald, Christopher","Tavakkoli, Alireza"],"dc:creator":["Galloway, Brian"],"dc:date.accessioned":["2025-09-08T18:49:13Z"],"dc:date.available":["2025-09-08T18:49:13Z"],"dc:date.issued":["2025"],"dc:description.abstract":["This thesis presents a remarkable result, that showcases an unexpected interplaybetween Riemannian geometry and symplectic topology on 4-manifolds. These two branches of mathematics belong to different worlds: Where geometry concerns it- self with distances, angles, areas, curvatures, etc., all of which typically vary from one point on the manifold to the next, topology studies properties of manifolds that are unaltered and remain constant when varying the metric. In this thesis we first provide a general overview of spin geometry on Riemannian manifolds and then es- tablish a fundamental restriction on the scalar curvature induced by the topology of a symplectic manifold."],"dc:format":["PDF"],"dc:identifier.uri":["https://scholarwolf.unr.edu/handle/11714/11605"],"dc:language":["English"],"dc:language.iso":["en_US"],"dc:subject":["Dirac operatior","scalar curvature","spin geometry","symplectic manifolds"],"dc:title":["Scalar Curvature Constraints on Symplectic 4-Manifolds"],"dc:type":["Thesis"],"thesis:degree_level":["Master's Degree"]},"updated_at":"2026-07-27T21:45:57Z"}