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arXiv · 1101.4818

An algebraic model for free rational G-spectra

J. P. C. Greenlees·B. E. Shipley
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Abstract

We show that for any compact Lie group $G$ with identity component $N$ and component group $W=G/N$, the category of free rational $G$-spectra is equivalent to the category of torsion modules over the twisted group ring $H^*(BN)[W]$. This gives an algebraic classification of rational $G$-equivariant cohomology theories on free $G$-spaces and a practical method for calculating the groups of natural transformations between them. This uses the methods of arXiv:1101.2511, and some readers may find the simpler context of the present paper highlights the main thread of the argument.

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J. P. C. Greenlees, B. E. Shipley. 2013-05-20. An algebraic model for free rational G-spectra. https://doi.org/10.1112/blms%2Fbdt066

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