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Title:Equivariant E-infinity algebras
Author(s):Smith, Mychael
Director of Research:Rezk, Charles
Doctoral Committee Chair(s):McCarthy, Randy
Doctoral Committee Member(s):Ando, Matthew; Heller, Jeremiah
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Equivariant
Homotopy theory
E-infinity algebra
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.
Issue Date:2017-11-28
Type:Text
URI:http://hdl.handle.net/2142/99207
Rights Information:Copyright 2017 Mychael Smith
Date Available in IDEALS:2018-03-13
Date Deposited:2017-12


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