Modèle minimal équivariant et formalité
We study the rational equivariant homotopy type of a topological space X equipped with an action of the group of integers modulo n . For n = pk (p prime, k a positive integer), we build an algebraic model which gives the rational equivariant homotopy type of X. The homotopical fixed-point set appears in the construction of a model of the fixed-points set. In general, this model is different from G. Triantafillou's model [Ti]. For n = p (p prime), we then give a notion of equivariant formality. We prove that this notion is equivalent to the formalizability of the inclusion of fixed-points set i: XzP -X. Examples and counterexamples of Zp-formal spaces are given.
Soit P un cone normal de l'espace de Banach reel E. On note par N la constante normale de P. On considere le probleme aux deux points limites: −x″=f(t, x), t∈I, x(0)=x(1)=θ ou I=[0,1] et f une application continue de I×P dans P. On etudie l'existence de solutions positives multiples