Encoding equivariant commutativity via operads
By Javier J. Guti'errez, David White. Algebraic and Geometric Topology, 2017
80 citations recorded by the source corpus.
In this paper, we prove a conjecture of Blumberg and Hill regarding the existence of $N_\infty$-operads associated to given sequences $\mathcal{F} = (\mathcal{F}_n)_{n \in \mathbb{N}}$ 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/45b238634a3167fd3883fb5714b748beb6acc7c0
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Citations in the corpus
- Genuine equivariant operads (2017, methodology): “ NF-operads of Blumberg-Hill can be built from the theory of genuine equivariant operads, thus proving Corollary IV. We start with an abstract argument, which has also been used by Gutierrez-White in [12]. Writing I = F(∅) for the initial equivariant operad in OpG(sSet), i.e. the operad consisting o”