Equivariant algebraic topology

Illman, Sören

Annales de l'Institut Fourier, Tome 23 (1973) no. 2, pp. 87-91.

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.

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.

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