BibTeX
@MISC{Greenlees_rationalo(2)-equivariant,
author = {J.P.C. Greenlees},
title = {Rational O(2)-Equivariant Cohomology Theories.},
year = {}
}
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Abstract
. We use Greenlees [1996, 1996a] to give a complete description of rational O(2)- equivariant cohomology theories. 1. Introduction. This paper presents an algebraic model for O(2)-equivariant rational cohomology theories. The main mathematical input is the model for SO(2)-equivariant theories given in Part I of Greenlees [1996], together with special cases of results on rational Mackey functors from Greenlees [1996a]. Using these ingredients, and the usual formal framework of equivariant homotopy, it is not hard to assemble the model. Nonetheless, several features of the model were unexpected to the author, so it seems desirable to illustrate the issues which arise in this simple case. An exactly analagous model can be given with the continuous quaternion group as the group of equivariance, but it is most unlikely that such an explicit model can be given for groups of larger rank. First, we should explain that the cohomology theories we refer to are those admitting suspension isomorp...
Keyphrases
equivariant cohomology theory analagous model explicit model equivariant theory continuous quaternion group main mathematical input usual formal framework rational mackey functors suspension isomorp simple case equivariant homotopy several feature complete description rational cohomology theory special case algebraic model
