Dimension globale et classe fondamentale d'un espace

Rami, Youssef

doi:10.5802/aif.1676

Rami, Youssef

Annales de l'Institut Fourier, Tome 49 (1999) no. 1, pp. 333-350.

Résumé
Abstract

L’algèbre de Pontryagin d’un espace $K$ -elliptique vérifie le théorème d’Auslander-Buchsbaum-Serre. Nous donnons ici plusieurs caractérisations des espaces $K$ -elliptiques tels que gldim( $H_{*} (Ω S; K)) < \infty$ et lorsque $(S, K)$ est dans le domaine d’Anick. Nous introduisons aussi une suite spectrale “impaire des $ℰ xt$ ” et complétons les résultats obtenus par A. Murillo dans le cas rationnel.

The Pontryagin algebra of a $K$ -elliptic space satisfy the Auslander-Buchsbaum-Serre theorem. We give some characterizations of the $K$ -elliptic spaces with $H_{*} (Ω S; K)$ of finite global dimension and with $(S, K)$ in the Anick range. We also introduce an “ $ℰ xt$ -odd” spectral sequence and complete the results obtained by A. Murillo in the rational case.

MR Zbl

DOI : 10.5802/aif.1676

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     author = {Rami, Youssef},
     title = {Dimension globale et classe fondamentale d'un espace},
     journal = {Annales de l'Institut Fourier},
     pages = {333--350},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {49},
     number = {1},
     year = {1999},
     doi = {10.5802/aif.1676},
     mrnumber = {2000c:55012},
     zbl = {0920.55009},
     language = {fr},
     url = {https://www.numdam.org/articles/10.5802/aif.1676/}
}

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Rami, Youssef. Dimension globale et classe fondamentale d'un espace. Annales de l'Institut Fourier, Tome 49 (1999) no. 1, pp. 333-350. doi : 10.5802/aif.1676. https://www.numdam.org/articles/10.5802/aif.1676/

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