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

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

Mar 01, 2021
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Abstract: In this paper, 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 analysing 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. Authors: Michael Stahlhauer (University of Bonn)

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