$G_\infty$-ring spectra and Moore spectra for $\beta$-rings
Abstract
In this paper, we introduce the notion of -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 -ring structure. Such -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.
Keywords
Cite
@article{arxiv.2007.14304,
title = {$G_\infty$-ring spectra and Moore spectra for $\beta$-rings},
author = {Michael Stahlhauer},
journal= {arXiv preprint arXiv:2007.14304},
year = {2023}
}
Comments
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