Dans le fibré de l'espace des lacets libres, la fibre n'est pas, en général, totalement non cohomologue a zéro.
Dénombrement des types de K-homotopie. Théorie de la déformation
Dolbeault homotopy theory and compact nilmanifolds
In this paper we study the degeneration of both the cohomology and the cohomotopy Frölicher spectral sequences in a special class of complex manifolds, namely the class of compact nilmanifolds endowed with a nilpotent complex structure. Whereas the cohomotopy spectral sequence is always degenerate for such a manifold, there exist many nilpotent complex structures on compact nilmanifolds for which the classical Frölicher spectral sequence does not collapse even at the second term.
Dualité d'Eckmann-Hilton à travers les modèles de Chen-Quillen-Sullivan