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Operads in unstable global homotopy theory

Miguel Barrero

Algebraic & Geometric Topology 23 (2023) 3293–3355
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–operads, a good generalization of E–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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