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Rezk, Charles McCarthy, Randy Ando, Matthew Heller, Jeremiah Smith, Mychael 2018-03-13T15:25:12Z 2018-03-13T15:25:12Z 2020-03-14T09:15:08Z 2017-11-28 2017-12 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. 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). No. of bitstreams: 3 SMITH-DISSERTATION-2017.pdf: 262755 bytes, checksum: 3c2e68a901342aea92e5149c246396ff (MD5) LICENSE.txt: 4210 bytes, checksum: 83796bfdcc4aa1d94ad9bdb1f5f68fce (MD5) PROQUEST_LICENSE.txt: 4556 bytes, checksum: ec0f8b17caf5eb4b90f01e8153b5f521 (MD5) Previous issue date: 2017-11-28 Embargo set by: Seth Robbins for item 105170 Lift date: 2020-03-13T15:25:40Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 105170 Lift date: 2020-03-13T15:28:52Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 105170 on 2020-03-14T09:15:08Z. application/pdf http://hdl.handle.net/2142/99207 en Copyright 2017 Mychael Smith Equivariant Homotopy theory E-infinity algebra Equivariant E-infinity algebras text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.