2020/04/03 by David Barnes, Barnes, David, Magdalena Kędziorek +1
Computer Science · Mathematics · #19A22 (Secondary) #55P42 #55P60 (Primary) 55Q91 #55P91 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2004.01566
openalex publication_date 2020/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.