Abstract
A solution of the problem of topological classification of real cubic fourfolds is given. It is proven that the real locus of a real non-singular cubic fourfold is diffeomorphic either to a connected sum ℝP4 #i(S2 × S2)#j(S1 × S3) or to a disjoint union ℝP4 ⊔ S4. La voie la plus courte et la meilleure entre deux vérités de domaine réel passe souvent par le domaine imaginaire.J. S. Hadamard, Essai sur la psychologie de l'invention dans le domainemathématique, Edition Gaithier-Villars, 1975, p. 114.
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