Dimension globale et classe fondamentale d'un espace
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 * (ΩS;K))< et lorsque (S,K) est dans le domaine d’Anick. Nous introduisons aussi une suite spectrale “impaire des 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 * (ΩS;K) of finite global dimension and with (S,K) in the Anick range. We also introduce an “ xt -odd” spectral sequence and complete the results obtained by A. Murillo in the rational case.

@article{AIF_1999__49_1_333_0,
     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},
     zbl = {0920.55009},
     mrnumber = {2000c:55012},
     language = {fr},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1676/}
}
TY  - JOUR
AU  - Rami, Youssef
TI  - Dimension globale et classe fondamentale d'un espace
JO  - Annales de l'Institut Fourier
PY  - 1999
SP  - 333
EP  - 350
VL  - 49
IS  - 1
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1676/
DO  - 10.5802/aif.1676
LA  - fr
ID  - AIF_1999__49_1_333_0
ER  - 
%0 Journal Article
%A Rami, Youssef
%T Dimension globale et classe fondamentale d'un espace
%J Annales de l'Institut Fourier
%D 1999
%P 333-350
%V 49
%N 1
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1676/
%R 10.5802/aif.1676
%G fr
%F AIF_1999__49_1_333_0
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://aif.centre-mersenne.org/articles/10.5802/aif.1676/

[1] D. Anick, Hopf algebras up to homotopy, J. Amer. Math. Soc., 2 (1989), 417-453. | MR | Zbl

[2] L. Bisiaux, Depth and Toomer's invariant, à paraître dans, Topology and its Applications. | Zbl

[3] Y. Félix, La dichotomie elliptique-hyperbolique en homotopie rationnelle, Astérisque, 176 (1989). | MR | Zbl

[4] Y. Félix and S. Halperin, Rational L-S category and its applications, Trans. Amer. Math. Soc., 273 (1982), 1-73. | MR | Zbl

[5] Y. Félix, S. Halperin and J.-M. Lemaire and J.-C. Thomas, Mod p loop space homology, Invent. Math., 95 (1989), 247-262. | MR | Zbl

[6] Y. Félix, S. Halperin and J.-M. Lemaire, The Ganea conjecture and the L-S category of Poincaré duality complexes, Preprint Univ. Nice (1997).

[7] Y. Félix, S. Halperin and J.-C. Thomas, The Homotopy Lie algebra for finite complexes, Publ. I.H.E.S., 56 (1983), 89-96. | Numdam

[8] Y. Félix, S. Halperin and J.-C. Thomas, Gorenstein spaces, Adv. in Maths, 71 (1988), 92-112. | MR | Zbl

[9] Y. Félix, S. Halperin and J.-C. Thomas, Elliptic Hopf algebras, J. London. Math. Soc., (2) 43 (1991), 545-555. | MR | Zbl

[10] Y. Félix, S. Halperin and J.-C. Thomas, Hopf algebres of polynomial growth, J. Algebra, 125 (1989), 408-417. | MR | Zbl

[11] Y. Félix, S. Halperin and J.-C. Thomas, Rational Homotopy Theory, Preprint Université d'Angers (1997). | Zbl

[12] Y. Félix, S. Halperin and J.-C. Thomas, Hopf algebras and a counterexample to a conjecture of Anick, J. of Algebra, 169 (1994), 176-193. | MR | Zbl

[13] Y. Félix, S. Halperin, C. Jacobson, C. Löfwall and J.-C. Thomas, The radical of the homotopy Lie algebra, Amer. J. Math., 110 (1988), 301-322. | MR | Zbl

[14] W.H. Greub, S. Halperin and J.R. Vanstone, Connexions, Curvatures and Cohomology, Vol. III, Academic Press, New York, 1975. | Zbl

[15] S. Halperin, Finiteness in the minimal models of Sullivan, Trans. Amer. Math. Soc., 230 (1977), 173-199. | MR | Zbl

[16] S. Halperin, Universal enveloping algebras and loop space homology, J. Pure Appl. Algebra, 83 (1992), 237-282. | MR | Zbl

[17] S. Halperin and J.-M. Lemaire, Notion of category in differential algebra, in Algebraic Topology — Rational Homotopy, Lecture Notes in Mathematics, 1318 (1988), 138-154. | MR | Zbl

[18] I. James, On category, in the sense of Lusternik-Schnirelmann, Topology, 17 (1978), 331-348. | Zbl

[19] A. Murillo, The evaluation map of some Gorenstien algebras, J. Pure. Appl. Algebra, 91 (1994), 209-218. | MR | Zbl

[20] A. Murillo, The Top cohomology class of certain spaces, J. Pure. App. Algebra, 84 (1993), 209-214. | MR | Zbl

[21] J.-P. Serre, Algèbre locale, Multiplicités, Lecture Notes in Mathematics, 11 (1975). | Zbl

[22] D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math., 47 (1978), 269-331. | Numdam | MR | Zbl

[23] G.H. Toomer, Lusternik-Schnirelmann category and the Moore spectral sequence, Math. Z., 138 (1974), 123-143. | MR | Zbl

Cité par Sources :