Encoding equivariant commutativity via operads

Gutiérrez, Javier J; White, David

doi:10.2140/agt.2018.18.2919

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Encoding equivariant commutativity via operads

Javier J Gutiérrez and David White

Algebraic & Geometric Topology 18 (2018) 2919–2962

DOI: 10.2140/agt.2018.18.2919

Abstract

We prove a conjecture of Blumberg and Hill regarding the existence of $N_{\infty}$ –operads associated to given sequences $ℱ = {(ℱ_{n})}_{n \in ℕ}$ of families of subgroups of $G \times Σ_{n}$ . For every such sequence, we construct a model structure on the category of $G$ –operads, and we use these model structures to define $E_{\infty}^{ℱ}$ –operads, generalizing the notion of an $N_{\infty}$ –operad, and to prove the Blumberg–Hill conjecture. We then explore questions of admissibility, rectification, and preservation under left Bousfield localization for these $E_{\infty}^{ℱ}$ –operads, obtaining some new results as well for $N_{\infty}$ –operads.

Keywords

model category, homotopy category, equivariant homotopy theory, equivariant spectra, operads

Mathematical Subject Classification 2010

Primary: 55P42, 55P48, 55P60, 55P91, 55U35

References

Publication

Received: 7 July 2017

Revised: 28 February 2018

Accepted: 20 March 2018

Published: 22 August 2018

Authors

Javier J Gutiérrez
Departament de Matemàtiques i Informàtica Universitat de Barcelona Barcelona Spain
http://www.ub.edu/topologia/gutierrez
David White
Department of Mathematics Denison University Granville, OH United States
http://personal.denison.edu/~whiteda

Volume 18, issue 5 (2018)