Algebraic & Geometric Topology

Encoding equivariant commutativity via operads

Javier J Gutiérrez and David White

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We prove a conjecture of Blumberg and Hill regarding the existence of N –operads associated to given sequences = ( n ) n of families of subgroups of G × 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 –operads, generalizing the notion of an N –operad, and to prove the Blumberg–Hill conjecture. We then explore questions of admissibility, rectification, and preservation under left Bousfield localization for these E –operads, obtaining some new results as well for N –operads.

Article information

Algebr. Geom. Topol., Volume 18, Number 5 (2018), 2919-2962.

Received: 7 July 2017
Revised: 28 February 2018
Accepted: 20 March 2018
First available in Project Euclid: 30 August 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P42: Stable homotopy theory, spectra 55P48: Loop space machines, operads [See also 18D50] 55P60: Localization and completion 55P91: Equivariant homotopy theory [See also 19L47] 55U35: Abstract and axiomatic homotopy theory

model category homotopy category equivariant homotopy theory equivariant spectra operads


Gutiérrez, Javier J; White, David. Encoding equivariant commutativity via operads. Algebr. Geom. Topol. 18 (2018), no. 5, 2919--2962. doi:10.2140/agt.2018.18.2919.

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