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

DOI10.2140/AGT.2023.23.87arXiv2007.14304MaRDI QIDQ6346021

Michael Stahlhauer

Publication date: 8 July 2020

Abstract: In this paper, we introduce the notion of $G_{i}nfty$-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 $G_{i}nfty$-ring structure. Such $G_{i}nfty$-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 $$-ring, thus providing a new perspective on the theory of $$-rings.

Mathematics Subject Classification ID

Frobenius induction, Burnside and representation rings (19A22) Equivariant homotopy theory in algebraic topology (55P91) Spectra with additional structure ((E_infty), (A_infty), ring spectra, etc.) (55P43) Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads (18C15) Equivariant operations and obstructions in algebraic topology (55S91)

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