Operads in unstable global homotopy theory

Barrero, Miguel

doi:10.2140/agt.2023.23.3293

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Operads in unstable global homotopy theory

Miguel Barrero

Algebraic & Geometric Topology 23 (2023) 3293–3355

DOI: 10.2140/agt.2023.23.3293

Abstract

We study operads in unstable global homotopy theory, which is the homotopy theory of spaces with compatible actions by all compact Lie groups. We show that the theory of these operads works remarkably well, as for example it is possible to give a model structure for the category of algebras over any such operad. We define global $E_{\infty}$ –operads, a good generalization of $E_{\infty}$ –operads to the global setting, and we give a rectification result for algebras over them.

Keywords

global homotopy theory, equivariant homotopy theory, operads, model structures

Mathematical Subject Classification

Primary: 55P91

References

Publication

Received: 4 October 2021

Revised: 24 January 2022

Accepted: 21 March 2022

Published: 26 September 2023

Authors

Miguel Barrero
Institute for Mathematics, Astrophysics and Particle Physics Radboud University Nijmegen Netherlands

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Volume 23, issue 7 (2023)