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2018

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/194371

Encoding equivariant commutativity via operads

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https://doi.org/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 $\mathcal{F}=\left(\mathcal{F}_n\right)_{n \in \mathbb{N}}$ 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.

Subject

Teoria de l'homotopia, Teoria de models

Subject (English)

Homotopy theory, Model theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

GUTIÉRREZ MARÍN, Javier J. and WHITE, David. Encoding equivariant commutativity via operads. Algebraic and Geometric Topology. 2018. Vol. 18, num. 5, pags. 2919-2962. ISSN 1472-2747. [consulted: 16 of August of 2026]. Available at: https://hdl.handle.net/2445/194371

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