Equivariant algebraic topology
Annales de l'Institut Fourier, Volume 23 (1973) no. 2, p. 87-91

Let $G$ be a topological group. We give the existence of an equivariant homology and cohomology theory, defined on the category of all $G$-pairs and $G$-maps, which both satisfy all seven equivariant Eilenberg-Steenrod axioms and have a given covariant and contravariant, respectively, coefficient system as coefficients.

In the case that $G$ is a compact Lie group we also define equivariant $CW$-complexes and mention some of their basic properties.

The paper is a short abstract and contains no proofs.

Soit $G$ un groupe topologique ; nous montrons l’existence des théories homologiques et cohomologiques équivariantes, définies sur la catégorie des $G$-paires et $G$-applications qui satisfont tous les sept axiomes équivariants d’Eilenberg-Steenrod et qui ont le système des coefficients covariants (resp. contrevariants) donné.

Dans le cas d’un groupe de Lie Compact $G$ nous définissons aussi les $CW$-complexes équivariants et nous donnons quelques-unes de leurs propriétés fondamentales.

Cet article est un bref résumé et ne contient aucune démonstration.

@article{AIF_1973__23_2_87_0,
author = {Illman, S\"oren},
title = {Equivariant algebraic topology},
journal = {Annales de l'Institut Fourier},
publisher = {Imprimerie Durand},
address = {28 - Luisant},
volume = {23},
number = {2},
year = {1973},
pages = {87-91},
doi = {10.5802/aif.458},
zbl = {0261.55007},
mrnumber = {50 \#11220},
language = {en},
url = {http://www.numdam.org/item/AIF_1973__23_2_87_0}
}

Illman, Sören. Equivariant algebraic topology. Annales de l'Institut Fourier, Volume 23 (1973) no. 2, pp. 87-91. doi : 10.5802/aif.458. http://www.numdam.org/item/AIF_1973__23_2_87_0/

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