Rational local systems and connected finite loop spaces
Peer reviewed, Journal article
Accepted version
Åpne
Permanent lenke
https://hdl.handle.net/11250/2730456Utgivelsesdato
2021Metadata
Vis full innførselSamlinger
- Institutt for matematiske fag [2353]
- Publikasjoner fra CRIStin - NTNU [37221]
Originalversjon
https://doi.org/10.1017/S0017089520000658Sammendrag
Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group always has an algebraic model. Based on this idea, we show that the category of rational local systems on a connected finite loop space always has a simple algebraic model. When the loop space arises from a connected compact Lie group, this recovers a special case of a result of Pol and Williamson about rational cofree G-spectra. More generally, we show that if K is a closed subgroup of a compact Lie group G such that the Weyl group WGK is connected, then a certain category of rational G-spectra “at K” has an algebraic model. For example, when K is the trivial group, this is just the category of rational cofree G-spectra, and this recovers the aforementioned result. Throughout, we pay careful attention to the role of torsion and complete categories.