We construct functors of generalized differential forms. In the case of nilpotent spaces of finite type, they determine the weak homotopy type of the spaces. Moreover they are equipped, in an elementary and natural way, with the action of cup-i products. Working with commutative algebras up to homotopy (viewed as algebras over a cofibrant resolution of the operad of commutative algebras), we show using these functors that the model of the fiber of a simplicial map is the cofiber of the algebraic model of this map.
Keywords. Modeles algebriques, formes differentielles, operades, suites spectrales
AMS subject classification. Primary: 18D50. Secondary: 55P43, 55P48, 55T99.
Submitted: 17 October 2001. Accepted: 1 February 2002. Published: 5 February 2002.
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