{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/97268"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/97268","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quasi-elliptic cohomology","abstract":"We introduce and study quasi-elliptic cohomology, a theory related to Tate K-theory but built over the ring $\\mathbb{Z}[q^{\\pm}]$. In Chapter 2 we build an orbifold version of the theory, inspired by Devoto's equivariant Tate K-theory. In Chapter 3 we construct power operation in the orbifold theory, and prove a version of Strickland's theorem on symmetric equivariant cohomology modulo transfer ideals. In Chapter 4 we construct representing spectra but show that they cannot assemble into a global spectrum in the usual sense. In Chapter 6 we construct a new global homotopy theory containing the classical theory. In Chapter 7 we show quasi-elliptic cohomology is a global theory in the new category.","abstract_html":"We introduce and study quasi-elliptic cohomology, a theory related to Tate K-theory but built over the ring \\mathbb{Z}[q\\pm]. In Chapter 2 we build an orbifold version of the theory, inspired by Devoto's equivariant Tate K-theory. In Chapter 3 we construct power operation in the orbifold theory, and prove a version of Strickland's theorem on symmetric equivariant cohomology modulo transfer ideals. In Chapter 4 we construct representing spectra but show that they cannot assemble into a global spectrum in the usual sense. In Chapter 6 we construct a new global homotopy theory containing the classical theory. In Chapter 7 we show quasi-elliptic cohomology is a global theory in the new category.","abstract_has_math":true,"creators":["Huan, Zhen"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rezk, Charles","McCarthy, Randy","Ando, Matthew","Stojanoska, Vesna"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-08-10T19:14:31Z","date_published":"2017-08-10T19:14:31Z","updated_at":"2026-07-22T22:24:32Z","subjects":["Quasi-elliptic cohomology","Tate K-theory","Power operation","Spectra","Global homotopy theory"],"languages":["en"],"rights":["Copyright 2017 Zhen Huan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/97268","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rezk, Charles","McCarthy, Randy","Ando, Matthew","Stojanoska, Vesna"]},{"key":"dc:creator","label":"Author","values":["Huan, Zhen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-08-10T19:14:31Z","2017-04-21","2017-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Quasi-elliptic cohomology","Tate K-theory","Power operation","Spectra","Global homotopy theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Zhen Huan"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/97268"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We introduce and study quasi-elliptic cohomology, a theory related to Tate K-theory but built over the ring $\\mathbb{Z}[q^{\\pm}]$. In Chapter 2 we build an orbifold version of the theory, inspired by Devoto's equivariant Tate K-theory. In Chapter 3 we construct power operation in the orbifold theory, and prove a version of Strickland's theorem on symmetric equivariant cohomology modulo transfer ideals. In Chapter 4 we construct representing spectra but show that they cannot assemble into a global spectrum in the usual sense. In Chapter 6 we construct a new global homotopy theory containing the classical theory. In Chapter 7 we show quasi-elliptic cohomology is a global theory in the new category.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Zhen Huan, accepted the attached license on 2017-03-09 at 16:04.","The student, Zhen Huan, submitted this Dissertation for approval on 2017-03-09 at 16:24.","This Dissertation was approved for publication on 2017-04-21 at 10:39.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10583 on 2017-08-10 at 13:37:55","Made available in DSpace on 2017-08-10T19:14:31Z (GMT). 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In Chapter 3 we construct power operation in the orbifold theory, and prove a version of Strickland's theorem on symmetric equivariant cohomology modulo transfer ideals. In Chapter 4 we construct representing spectra but show that they cannot assemble into a global spectrum in the usual sense. In Chapter 6 we construct a new global homotopy theory containing the classical theory. In Chapter 7 we show quasi-elliptic cohomology is a global theory in the new category.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Zhen Huan, accepted the attached license on 2017-03-09 at 16:04.","The student, Zhen Huan, submitted this Dissertation for approval on 2017-03-09 at 16:24.","This Dissertation was approved for publication on 2017-04-21 at 10:39.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10583 on 2017-08-10 at 13:37:55","Made available in DSpace on 2017-08-10T19:14:31Z (GMT). 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