Algebraic and Geometric Topology 2 (2002), paper no. 5, pages 51-93.

Formes differentielles generalisees sur une operade et modeles algebriques des fibrations

David Chataur

Abstract. On construit des foncteurs de formes differentielles generalisees. Ceux-ci, dans le cas d'espaces nilpotents de type fini, determinent le type d'homotopie faible des espaces. Ils sont munis, d'une maniere elementaire et naturelle, de l'action de cup-i produits. Pour les algebres commutatives a homotopit pres (algebres sur une resolution cofibrante de l'operade des slgebres commutatives), on demontre en utilisant les formes differentielles generalisees que le modele de la fibre d'une application simpliciale est la cofibre du modele de ce morphisme.

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.

DOI: 10.2140/agt.2002.2.51

E-print: arXiv:math.AT/0202262

Submitted: 17 October 2001. Accepted: 1 February 2002. Published: 5 February 2002.

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David Chataur
Centre di Recerca Matematica, Institut d'Estudis Catalans
Apartat 50 E - 08193 Bellaterra, Spain
Email: dchataur@crm.es

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