Dimension globale et classe fondamentale d'un espace

Rami, Youssef

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

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($H_{*}(\Omega S;K))<\infty$ et lorsque $(S,K)$ est dans le domaine d’Anick. Nous introduisons aussi une suite spectrale “impaire des $ℰ\mathrm{xt}$” 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 $H_{*}(\Omega S;K)$ of finite global dimension and with $(S,K)$ in the Anick range. We also introduce an “$ℰ\mathrm{xt}$-odd” spectral sequence and complete the results obtained by A. Murillo in the rational case.

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