An introduction to algebraic models for rational G-spectra
Abstract
The project of Greenlees et al. on understanding rational G-spectra in terms of algebraic categories has had many successes, classifying rational G-spectra for finite groups, SO(2), O(2), SO(3), free and cofree G-spectra as well as rational toral G-spectra for arbitrary compact Lie groups. This paper provides an introduction to the subject in two parts. The first discusses rational G-Mackey functors, the action of the Burnside ring and change of group functors. It gives a complete proof of the well-known classification of rational Mackey functors for finite G. The second part discusses the methods and tools from equivariant stable homotopy theory needed to obtain algebraic models for rational G-spectra. It gives a summary of the key steps in the classification of rational G-spectrain terms of a symmetric monoidal algebraic category. Having these two parts in the same place allows one to clearly see the analogy between the algebraic and topological classifications.
Cite
@article{arxiv.2004.01566,
title = {An introduction to algebraic models for rational G-spectra},
author = {David Barnes and Magdalena Kedziorek},
journal= {arXiv preprint arXiv:2004.01566},
year = {2021}
}
Comments
41 pages, further examples added. Accepted for publication in the Proceedings of the 2019 Equivariant Topology & Derived Algebra Conference