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On $G$-disconnected injective models

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On G-disconnected injective models AN N A L E S D E L’INSTI T U T F O U R IE R ANNALES DE L’INSTITUT FOURIER Marek GOLASIN´SKI On G-disconnected injective models Tome 53, no 2 (2003), p. 625-664. <> © Association des Annales de l’institut Fourier, 2003, tous droits réservés. L’accès aux articles de la revue « Annales de l’institut Fourier » (, implique l’accord avec les conditions générales d’utilisation ( Toute re- production en tout ou partie cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement per- sonnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. cedram Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques 625 ON G-DISCONNECTED INJECTIVE MODELS by Marek GOLASI0144SKI Ann. Inst. Fourier, Grenoble 53, 2 (2003), 625-664 Introduction. The purpose of this paper is to redefine the equivariant minimal- ity and redevelop some results on the rational homotopy theory of G- disconnected spaces. This was originally studied by the author in [7] but some of the constructions used must be corrected. The central results of Sullivan’s theory of minimal models [18] has been generalized by Triantafillou [19], [20] to equivariant simply connected and nilpotent spaces when G is finite, but only to G-connected and finite type spaces. Since a space X is G-connected only if all the fixed point subspaces X H are non-empty and connected for all subgroups H C G, this is a very restrictive condition. To model these equivariant spaces it is necessary to use not only the de Rham algebra Ax of Q-differential forms on X but also a functor Ax on the orbit category which contains all of the algebras AX H for all subgroups H C G. The key to producing equi

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