Algebraic & Geometric Topology

Formes différentielles généralisées sur une opérade et modèles algébriques des fibrations

David Chataur

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Abstract

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.

Resum é

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.

Article information

Source
Algebr. Geom. Topol., Volume 2, Number 1 (2002), 51-93.

Dates
Received: 17 October 2001
Accepted: 1 February 2002
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882685

Digital Object Identifier
doi:10.2140/agt.2002.2.51

Mathematical Reviews number (MathSciNet)
MR1885216

Zentralblatt MATH identifier
0994.18005

Subjects
Primary: 18D50: Operads [See also 55P48]
Secondary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55P48: Loop space machines, operads [See also 18D50] 55T99: None of the above, but in this section

Keywords
modèles algébriques formes différentielles opérades suites spectrales

Citation

Chataur, David. Formes différentielles généralisées sur une opérade et modèles algébriques des fibrations. Algebr. Geom. Topol. 2 (2002), no. 1, 51--93. doi:10.2140/agt.2002.2.51. https://projecteuclid.org/euclid.agt/1513882685


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