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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.01566
- arXiv:
- arXiv:2004.01566
- Bibcode:
- 2020arXiv200401566B
- Keywords:
-
- Mathematics - Algebraic Topology;
- Mathematics - Representation Theory;
- 55P91;
- 55P42;
- 55P60 (Primary) 55Q91;
- 19A22 (Secondary)
- E-Print:
- 41 pages, further examples added. Accepted for publication in the Proceedings of the 2019 Equivariant Topology &