# name
Encoding equivariant commutativity via operads

# metadata.dc.description.abstract[].value
We prove a conjecture of Blumberg and Hill regarding the existence of $N_{\infty}$-operads associated to given sequences $\mathcal{F}=\left(\mathcal{F}_n\right)_{n \in \mathbb{N}}$ of families of subgroups of $G \times \Sigma_n$. For every such sequence, we construct a model structure on the category of $G-$ operads, and we use these model structures to define $E_{\infty}^{\mathcal{F}}$-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 $E_{\infty}^{\mathcal{F}}$-operads, obtaining some new results as well for $N_{\infty}^{-}$ operads.

# metadata.dc.relation.ispartof[].value
Algebraic and Geometric Topology, 2018, vol. 18, num. 5, p. 2919-2962

# metadata.dc.rights[].value
(c) Mathematical Sciences Publishers, 2018

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Encoding equivariant commutativity via operads