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

Abstract

In this paper, 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 analysing 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 $\beta$-ring, thus providing a new perspective on the theory of $\beta$-rings.

50 pages. Revised version of Master's Thesis written at the University of Bonn. Accepted for publication in Algebraic & Geometric Topology. v3: Corrections and clarifications in response to referee report. In particular, the discussion of cohomotopy and the conditions on the deflation pairing in Chapter 3 have been expanded

References in corpus (4)

• Global homotopy theory
• Model Structures on Commutative Monoids in General Model Categories
• Global Mackey functors with operations and n-special lambda rings
• Adams operations in cohomotopy