{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/99207"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/99207","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Equivariant E-infinity algebras","abstract":"The equivariant 𝔼∞G operad has the property that 𝔼∞G(n) is the total space for the G-equivariant universal principal Σn bundle. There is a forgetful functor from 𝔼∞G-algebras to 𝔼∞-algebras, where 𝔼∞ is the classic 𝔼∞ operad. This functor admits a homotopical right adjoint R. The goal of this thesis is to understand R by expressing the free 𝔼∞G-algebra on a G-space X as a homotopy colimit of classic 𝔼∞ algebras.","abstract_html":"The equivariant 𝔼∞G operad has the property that 𝔼∞G(n) is the total space for the G-equivariant universal principal Σn bundle. There is a forgetful functor from 𝔼∞G-algebras to 𝔼∞-algebras, where 𝔼∞ is the classic 𝔼∞ operad. This functor admits a homotopical right adjoint R. The goal of this thesis is to understand R by expressing the free 𝔼∞G-algebra on a G-space X as a homotopy colimit of classic 𝔼∞ algebras.","abstract_has_math":false,"creators":["Smith, Mychael"],"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","Heller, Jeremiah"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-03-13T15:25:12Z","date_published":"2018-03-13T15:25:12Z","updated_at":"2026-07-22T22:24:37Z","subjects":["Equivariant","Homotopy theory","E-infinity algebra"],"languages":["en"],"rights":["Copyright 2017 Mychael Smith"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/99207","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","Heller, Jeremiah"]},{"key":"dc:creator","label":"Author","values":["Smith, Mychael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-03-13T15:25:12Z","2020-03-14T09:15:08Z","2017-11-28","2017-12"]},{"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":["Equivariant","Homotopy theory","E-infinity algebra"]}]},{"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 Mychael Smith"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/99207"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The equivariant 𝔼∞G operad has the property that 𝔼∞G(n) is the total space for the G-equivariant universal principal Σn bundle. 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There is a forgetful functor from 𝔼∞G-algebras to 𝔼∞-algebras, where 𝔼∞ is the classic 𝔼∞ operad. This functor admits a homotopical right adjoint R. The goal of this thesis is to understand R by expressing the free 𝔼∞G-algebra on a G-space X as a homotopy colimit of classic 𝔼∞ algebras.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2019-12-01","The student, Mychael Smith, accepted the attached license on 2017-11-27 at 11:33.","The student, Mychael Smith, submitted this Dissertation for approval on 2017-11-27 at 11:40.","This Dissertation was approved for publication on 2017-11-28 at 12:43.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11758 on 2018-03-13 at 09:55:53","Made available in DSpace on 2018-03-13T15:25:12Z (GMT). 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