{"id":{"repo_id":"cornell","oai_identifier":"oai:ecommons.cornell.edu:1813/67332"},"canonical_url":"https://search.dev.ndltd.org/etd/cornell/oai:ecommons.cornell.edu:1813/67332","repository":{"repo_id":"cornell","name":"Cornell University","base_url":"https://ecommons.cornell.edu/server/oai/request"},"display":{"title":"The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds","abstract":"This is a collection of algebraic topological results for toric origami manifolds, mostly in dimension 4. Using a known formula for the fundamental group of a compact orientable toric origami manifold, a list of all groups obtainable as the fundamental group of a compact orientable toric origami 4-manifold is given, along with example manifolds that realize them. The known fundamental group formula is generalized to compact non-orientable toric origami manifolds of all dimensions. The homology and cohomology groups of toric origami 4-manifolds are explicitly constructed with generators realized as embedded submanifolds, and the intersection form and cohomology ring are calculated.","abstract_html":"This is a collection of algebraic topological results for toric origami manifolds, mostly in dimension 4. Using a known formula for the fundamental group of a compact orientable toric origami manifold, a list of all groups obtainable as the fundamental group of a compact orientable toric origami 4-manifold is given, along with example manifolds that realize them. The known fundamental group formula is generalized to compact non-orientable toric origami manifolds of all dimensions. The homology and cohomology groups of toric origami 4-manifolds are explicitly constructed with generators realized as embedded submanifolds, and the intersection form and cohomology ring are calculated.","abstract_has_math":false,"creators":["Pendleton, Ian Alexander"],"institution":"Cornell University","degree_name":"Ph.D., Mathematics","degree_level":"Doctor of Philosophy","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":["Sjamaar, Reyer","Manning, Jason F."],"year":2019,"date_issued":"2019-05-30","date_published":"2019-05-30","updated_at":"2026-07-24T01:49:00Z","subjects":["algebraic topology","toric origami","toric symplectic","Mathematics","symplectic geometry"],"languages":["en_US"],"rights":["Attribution 4.0 International"],"rights_urls":["https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7298/4nc1-3039"],"render_values":[{"text":"https://doi.org/10.7298/4nc1-3039","href":"https://doi.org/10.7298/4nc1-3039","code":true}]},{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["ProQuest Submission ID: 11441","ProQuest Publication ID: 13883378"],"render_values":[{"text":"ProQuest Submission ID: 11441","href":null,"code":true},{"text":"ProQuest Publication ID: 13883378","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/1813/67332","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Sjamaar, Reyer","Manning, Jason F."]},{"key":"dc:creator","label":"Author","values":["Pendleton, Ian Alexander"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-10-15T15:30:02Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-10-15T15:30:02Z"]},{"key":"dc:date.issued","label":"Date","values":["2019-05-30"]},{"key":"dc:type","label":"Dc Type","values":["dissertation or thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctor of Philosophy"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D., Mathematics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Cornell University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["algebraic topology","toric origami","toric symplectic","Mathematics","symplectic geometry"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["Attribution 4.0 International"]},{"key":"dc:rights.uri","label":"Rights URI","values":["https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7298/4nc1-3039"]},{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["ProQuest Submission ID: 11441","ProQuest Publication ID: 13883378"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1813/67332"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This is a collection of algebraic topological results for toric origami manifolds, mostly in dimension 4. Using a known formula for the fundamental group of a compact orientable toric origami manifold, a list of all groups obtainable as the fundamental group of a compact orientable toric origami 4-manifold is given, along with example manifolds that realize them. The known fundamental group formula is generalized to compact non-orientable toric origami manifolds of all dimensions. The homology and cohomology groups of toric origami 4-manifolds are explicitly constructed with generators realized as embedded submanifolds, and the intersection form and cohomology ring are calculated."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds"]}]}],"canonical_facts":{"dc:contributor.committeemember":["Sjamaar, Reyer","Manning, Jason F."],"dc:creator":["Pendleton, Ian Alexander"],"dc:date.accessioned":["2019-10-15T15:30:02Z"],"dc:date.available":["2019-10-15T15:30:02Z"],"dc:date.issued":["2019-05-30"],"dc:description.abstract":["This is a collection of algebraic topological results for toric origami manifolds, mostly in dimension 4. Using a known formula for the fundamental group of a compact orientable toric origami manifold, a list of all groups obtainable as the fundamental group of a compact orientable toric origami 4-manifold is given, along with example manifolds that realize them. The known fundamental group formula is generalized to compact non-orientable toric origami manifolds of all dimensions. The homology and cohomology groups of toric origami 4-manifolds are explicitly constructed with generators realized as embedded submanifolds, and the intersection form and cohomology ring are calculated."],"dc:format.mimetype":["application/pdf"],"dc:identifier.doi":["https://doi.org/10.7298/4nc1-3039"],"dc:identifier.other":["ProQuest Submission ID: 11441","ProQuest Publication ID: 13883378"],"dc:identifier.uri":["https://hdl.handle.net/1813/67332"],"dc:language.iso":["en_US"],"dc:rights":["Attribution 4.0 International"],"dc:rights.uri":["https://creativecommons.org/licenses/by/4.0/"],"dc:subject":["algebraic topology","toric origami","toric symplectic","Mathematics","symplectic geometry"],"dc:title":["The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds"],"dc:type":["dissertation or thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctor of Philosophy"],"thesis:degree_name":["Ph.D., Mathematics"],"thesis:institution_name":["Cornell University"]},"updated_at":"2026-07-24T01:49:00Z"}