Equivariant E-infinity algebras

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Smith, Mychael

Contributors dc:contributor

• Rezk, Charles
• McCarthy, Randy
• Ando, Matthew
• Heller, Jeremiah

• Equivariant
• Homotopy theory
• E-infinity algebra

Statement dc:rights

• Copyright 2017 Mychael Smith

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/99207