Director of Research (if dissertation) or Advisor (if thesis)
Rezk, Charles
Doctoral Committee Chair(s)
McCarthy, Randy
Committee Member(s)
Ando, Matthew
Heller, Jeremiah
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Equivariant
Homotopy theory
E-infinity algebra
Abstract
The equivariant đŒâG operad has the property that đŒâG(n) is the total space for the G-equivariant universal principal ÎŁn bundle. There is a forgetful functor from đŒâG-algebras to đŒâ-algebras, where đŒâ is the classic đŒâ operad. This functor admits a homotopical right adjoint R. The goal of this thesis is to understand R by expressing the free đŒâG-algebra on a G-space X as a homotopy colimit of classic đŒâ algebras.
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