Si est un groupe fini, L.S. Scull a observé que la définition originale de la minimalité équivariante n’est pas correcte dans le cas -connexe par suite d’une erreur concernant des propriétés algébriques. Dans le cas -non connexe la catégorie des orbites a été remplacée par la catégorie , avec un objet pour chaque composante des sous-ensembles simpliciaux de points fixes d’un ensemble -simplicial , pour tous les sous-groupes . Nous redéfinissons la minimalité équivariante et nous redéveloppons des résultats d’homotopie rationnelle pour les ensembles -simpliciaux non connexes. Pour montrer l’existence d’un modèle minimal injectif pour un ensemble -simplicial non connexe, nous remplaçons par la catégorie plus subtile avec un objet pour chaque 0-simplexe de sous-ensembles simpliciaux de points fixes , par tous les sous- groupes .
Let be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the -connected case is incorrect because of an error concerning algebraic properties. In the -disconnected case the orbit category was originally replaced by the category with one object for each component of each fixed point simplicial subsets of a -simplicial set , for all subgroups . We redefine the equivariant minimality and redevelop some results on the rational homotopy theory of disconnected -simplicial sets. To show an existence of the injective minimal model for a disconnected -simplicial set we replace by the more subtle category with one object for each 0-simplex of fixed point simplicial subsets , for all subgroups .
@article{AIF_2003__53_2_625_0, author = {Golasi\'nski, Marek}, title = {On $G$-disconnected injective models}, journal = {Annales de l'Institut Fourier}, volume = {53}, year = {2003}, pages = {625-664}, doi = {10.5802/aif.1954}, mrnumber = {1990008}, zbl = {01940706}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_2003__53_2_625_0} }
Golasiński, Marek. On $G$-disconnected injective models. Annales de l'Institut Fourier, Tome 53 (2003) pp. 625-664. doi : 10.5802/aif.1954. http://gdmltest.u-ga.fr/item/AIF_2003__53_2_625_0/
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