{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/16822"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/16822","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Torus equivariant elliptic cohomology and sigma orientations","abstract":"Let $ \\mathcal{C} \\colon= \\mathds{C}/ \\Lambda$ be a complex elliptic curve. In this paper, we give a detailed construction of torus equivariant elliptic cohomology, which is a sheaf of $ \\mathcal{ O}_{\\mathcal{C}^n}$-algebras over $ \\mathcal{C}^n$. As applications, we construct global sections for sigma functions and relates these sections to the elliptic orbifold genera.","abstract_html":"Let $ \\mathcal{C} \\colon= \\mathds{C}/ \\Lambda$ be a complex elliptic curve. In this paper, we give a detailed construction of torus equivariant elliptic cohomology, which is a sheaf of <span class=\"etd-inline-math\"> \\mathcal{ O}<sub>\\mathcal{C}<sup>n</sup></sub></span>-algebras over <span class=\"etd-inline-math\"> \\mathcal{C}<sup>n</sup></span>. As applications, we construct global sections for sigma functions and relates these sections to the elliptic orbifold genera.","abstract_has_math":true,"creators":["Chen, Hsian-Yang"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ando, Matthew","Rezk, Charles","McCarthy, Randy","Guillou, Bertrand"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-08-20T17:58:52Z","date_published":"2010-08-20T17:58:52Z","updated_at":"2026-07-22T22:25:09Z","subjects":["elliptic cohomology","sigma orientation"],"languages":["en"],"rights":["Copyright 2010 Hsian-Yang Chen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/16822","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ando, Matthew","Rezk, Charles","McCarthy, Randy","Guillou, Bertrand"]},{"key":"dc:creator","label":"Author","values":["Chen, Hsian-Yang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-08-20T17:58:52Z","2010-08"]},{"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":["elliptic cohomology","sigma orientation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Hsian-Yang Chen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/16822"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Let $ \\mathcal{C} \\colon= \\mathds{C}/ \\Lambda$ be a complex elliptic curve. In this paper, we give a detailed construction of torus equivariant elliptic cohomology, which is a sheaf of $ \\mathcal{ O}_{\\mathcal{C}^n}$-algebras over $ \\mathcal{C}^n$. As applications, we construct global sections for sigma functions and relates these sections to the elliptic orbifold genera.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-28T15:51:58Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Chen_Hsian-Yang.pdf: 832894 bytes, checksum: 57eea2381b888da8f8a50578102293ed (MD5)","Made available in DSpace on 2010-08-20T17:58:52Z (GMT). No. of bitstreams: 2 Chen_Hsian-Yang.pdf: 832894 bytes, checksum: 57eea2381b888da8f8a50578102293ed (MD5) license.txt: 4058 bytes, checksum: d55ad5a4f9792864694cebe8d6420243 (MD5)"]},{"key":"dc:title","label":"Title","values":["Torus equivariant elliptic cohomology and sigma orientations"]}]}],"canonical_facts":{"dc:contributor":["Ando, Matthew","Rezk, Charles","McCarthy, Randy","Guillou, Bertrand"],"dc:creator":["Chen, Hsian-Yang"],"dc:date":["2010-08-20T17:58:52Z","2010-08"],"dc:description":["Let $ \\mathcal{C} \\colon= \\mathds{C}/ \\Lambda$ be a complex elliptic curve. In this paper, we give a detailed construction of torus equivariant elliptic cohomology, which is a sheaf of $ \\mathcal{ O}_{\\mathcal{C}^n}$-algebras over $ \\mathcal{C}^n$. As applications, we construct global sections for sigma functions and relates these sections to the elliptic orbifold genera.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-28T15:51:58Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Chen_Hsian-Yang.pdf: 832894 bytes, checksum: 57eea2381b888da8f8a50578102293ed (MD5)","Made available in DSpace on 2010-08-20T17:58:52Z (GMT). No. of bitstreams: 2 Chen_Hsian-Yang.pdf: 832894 bytes, checksum: 57eea2381b888da8f8a50578102293ed (MD5) license.txt: 4058 bytes, checksum: d55ad5a4f9792864694cebe8d6420243 (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/16822"],"dc:language":["en"],"dc:rights":["Copyright 2010 Hsian-Yang Chen"],"dc:subject":["elliptic cohomology","sigma orientation"],"dc:title":["Torus equivariant elliptic cohomology and sigma orientations"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:09Z"}