{"id":{"repo_id":"oregon","oai_identifier":"oai:scholarsbank.uoregon.edu:1794/23748"},"canonical_url":"https://search.dev.ndltd.org/etd/oregon/oai:scholarsbank.uoregon.edu:1794/23748","repository":{"repo_id":"oregon","name":"University of Oregon","base_url":"https://scholarsbank.uoregon.edu/server/oai/request"},"display":{"title":"A Structure Theorem for RO(C2)-graded Cohomology","abstract":"Let C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)-graded Bredon cohomology of C2-spaces using coefficients in the constant Mackey functor F2. We show that, as a module over the cohomology of the point, the RO(C2)-graded cohomology of a finite C2-CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action. The shifts are by elements of RO(C2) corresponding to actual (i.e. non-virtual) C2-representations.","abstract_html":"Let C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)-graded Bredon cohomology of C2-spaces using coefficients in the constant Mackey functor F2. We show that, as a module over the cohomology of the point, the RO(C2)-graded cohomology of a finite C2-CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action. The shifts are by elements of RO(C2) corresponding to actual (i.e. non-virtual) C2-representations.","abstract_has_math":false,"creators":["May, Clover"],"institution":"University of Oregon","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":"Department of Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Dugger, Daniel"],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-06","date_published":"2018-09-06","updated_at":"2026-08-21T16:47:20Z","subjects":[],"languages":["en_US"],"rights":["All Rights Reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1794/23748","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F23748","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Dugger, Daniel"]},{"key":"dc:creator","label":"Author","values":["May, Clover"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-09-06T21:56:46Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-09-06T21:56:46Z"]},{"key":"dc:date.issued","label":"Date","values":["2018-09-06"]},{"key":"dc:publisher","label":"Institution","values":["University of Oregon"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Oregon"]}]},{"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":["All Rights Reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1794/23748"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)-graded Bredon cohomology of C2-spaces using coefficients in the constant Mackey functor F2. We show that, as a module over the cohomology of the point, the RO(C2)-graded cohomology of a finite C2-CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action. The shifts are by elements of RO(C2) corresponding to actual (i.e. non-virtual) C2-representations."]},{"key":"dc:title","label":"Title","values":["A Structure Theorem for RO(C2)-graded Cohomology"]}]}],"canonical_facts":{"dc:contributor.advisor":["Dugger, Daniel"],"dc:creator":["May, Clover"],"dc:date.accessioned":["2018-09-06T21:56:46Z"],"dc:date.available":["2018-09-06T21:56:46Z"],"dc:date.issued":["2018-09-06"],"dc:description.abstract":["Let C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)-graded Bredon cohomology of C2-spaces using coefficients in the constant Mackey functor F2. We show that, as a module over the cohomology of the point, the RO(C2)-graded cohomology of a finite C2-CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action. The shifts are by elements of RO(C2) corresponding to actual (i.e. non-virtual) C2-representations."],"dc:identifier.uri":["https://hdl.handle.net/1794/23748"],"dc:language.iso":["en_US"],"dc:publisher":["University of Oregon"],"dc:rights":["All Rights Reserved."],"dc:title":["A Structure Theorem for RO(C2)-graded Cohomology"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Department of Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Oregon"]},"updated_at":"2026-08-21T16:47:20Z"}