University of Illinois Urbana-Champaign

Equivariant E-infinity algebras

Smith, Mychael

Content Files
SMITH-DISSERTATION-2017.pdf

Permalink

https://hdl.handle.net/2142/99207

Description

Title
Equivariant E-infinity algebras
Author(s)
Smith, Mychael
Issue Date
2017-11-28
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
Date of Ingest
2018-03-13T15:25:12Z
Keyword(s)
  • Equivariant
  • Homotopy theory
  • E-infinity algebra
Abstract
The equivariant š”¼āˆžG operad has the property that š”¼āˆžG(n) is the total space for the G-equivariant universal principal Ī£n bundle. There is a forgetful functor from š”¼āˆžG-algebras to š”¼āˆž-algebras, where š”¼āˆž is the classic š”¼āˆž operad. This functor admits a homotopical right adjoint R. The goal of this thesis is to understand R by expressing the free š”¼āˆžG-algebra on a G-space X as a homotopy colimit of classic š”¼āˆž algebras.
Graduation Semester
2017-12
Type of Resource
text
Permalink
http://hdl.handle.net/2142/99207
Copyright and License Information
Copyright 2017 Mychael Smith

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