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Rational \(\text{SO}(3)\)-equivariant cohomology theories. (English) Zbl 0995.55001

Greenlees, J. P. C. (ed.) et al., Homotopy methods in algebraic topology. Proceedings of an AMS-IMS-SIAM joint summer research conference, University of Colorado, Boulder, CO, USA, June 20-24, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 271, 99-125 (2001).
The paper gives a complete classification of rational \(SO(3)\)-equivariant cohomology theories. This is done by presenting an algebraic model for \(SO(3)\)-equivariant rational cohomology theories. More precisely, some of the author’s earlier results are used to give an explicit algebraic model of the category of rational \(SO(3)\)-spectra. The results include an algebraic model for \(SO(2)\)-equivariant theories and an analysis of \(O(2)\)-equivariant cohomology theories together with special cases of results on rational Mackey functors.
For the entire collection see [Zbl 0964.00013].

MSC:

55N91 Equivariant homology and cohomology in algebraic topology
55P42 Stable homotopy theory, spectra
55P91 Equivariant homotopy theory in algebraic topology
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