Formes différentielles généralisées sur une opérade et modèles algébriques des fibrations

Chataur, David¹

¹Centre di Recerca Matemática, Institut d’Estudis Catalans, Apartat 50 E, 08193 Bellaterra, Spain

Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 51-93

Résumé

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.

Resumé

On construit des foncteurs de formes différentielles généralisées. Ceux-ci, dans le cas d’espaces nilpotents de type fini, déterminent le type d’homotopie faible des espaces. Ils sont munis, d’une manière élémentaire et naturelle, de l’action de cup-i produits. Pour les algèbres commutatives à homotopit prés (algèbres sur une résolution cofibrante de l’opérade des algèbres commutatives), on démontre en utilisant les formes différentielles généralisées que le modèle de la fibre d’une application simpliciale est la cofibre du modèle de ce morphisme.

Détail

DOI : 10.2140/agt.2002.2.51

Keywords: modèles algébriques, formes différentielles, opérades, suites spectrales

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