## Algebraic & Geometric Topology

### Encoding equivariant commutativity via operads

#### Abstract

We prove a conjecture of Blumberg and Hill regarding the existence of $N ∞$–operads associated to given sequences $ℱ = ( ℱ n ) n ∈ ℕ$ 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 $E ∞ ℱ$–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 $E ∞ ℱ$–operads, obtaining some new results as well for $N ∞$–operads.

#### Article information

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

Dates
Revised: 28 February 2018
Accepted: 20 March 2018
First available in Project Euclid: 30 August 2018

https://projecteuclid.org/euclid.agt/1535594427

Digital Object Identifier
doi:10.2140/agt.2018.18.2919

Mathematical Reviews number (MathSciNet)
MR3848404

Zentralblatt MATH identifier
06935825

#### Citation

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. https://projecteuclid.org/euclid.agt/1535594427

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