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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