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$G_\infty$–ring spectra and Moore spectra for $\beta$–rings

Michael Stahlhauer

Algebraic & Geometric Topology 23 (2023) 87–153
Abstract

We introduce the notion of G–ring spectra. These are globally equivariant homotopy types with a structured multiplication, giving rise to power operations on their equivariant homotopy and cohomology groups. We illustrate this structure by analyzing when a Moore spectrum can be endowed with a G–ring structure. Such G–structures correspond to power operations on the underlying ring, indexed by the Burnside ring. We exhibit a close relation between these globally equivariant power operations and the structure of a β–ring, thus providing a new perspective on the theory of β–rings.

Keywords
structured ring spectra, equivariant homotopy theory, beta-rings, power operations
Mathematical Subject Classification
Primary: 55P43, 55P91
Secondary: 18C15, 19A22, 55S91
References
Publication
Received: 22 September 2020
Revised: 22 July 2021
Accepted: 3 November 2021
Published: 27 March 2023
Authors
Michael Stahlhauer
Max Planck Institute for Mathematics
Bonn
Germany
https://guests.mpim-bonn.mpg.de/stahlhauer/

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