G∞–ring spectra and Moore spectra for β–rings

Stahlhauer, Michael

doi:10.2140/agt.2023.23.87

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

Michael Stahlhauer

Algebraic & Geometric Topology 23 (2023) 87–153

DOI: 10.2140/agt.2023.23.87

Abstract

We introduce the notion of $G_{\infty}$ –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 $G_{\infty}$ –ring structure. Such $G_{\infty}$ –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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Volume 23, issue 1 (2023)