Homologie des espaces de lacets des espaces de configuration
Annales de l'Institut Fourier, Volume 44 (1994) no. 2, pp. 559-568.

We compute the loop space homology of the space F(M,k) of configurations of k points in a compact simply connected manifold M. We prove in particular that, if H * (M,) is not generated by one generator, then the rational homology of ΩF(M,k) contains a tensor algebra for k2.

Nous calculons dans ce texte l’homologie de l’espace des lacets de l’espace des configurations ordonnées de k points dans une variété compacte simplement connexe M.

@article{AIF_1994__44_2_559_0,
     author = {F\'elix, Yves and Thomas, Jean-Claude},
     title = {Homologie des espaces de lacets des espaces de configuration},
     journal = {Annales de l'Institut Fourier},
     pages = {559--568},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {44},
     number = {2},
     year = {1994},
     doi = {10.5802/aif.1409},
     mrnumber = {95i:55007},
     zbl = {0806.57024},
     language = {fr},
     url = {http://archive.numdam.org/articles/10.5802/aif.1409/}
}
TY  - JOUR
AU  - Félix, Yves
AU  - Thomas, Jean-Claude
TI  - Homologie des espaces de lacets des espaces de configuration
JO  - Annales de l'Institut Fourier
PY  - 1994
SP  - 559
EP  - 568
VL  - 44
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.1409/
DO  - 10.5802/aif.1409
LA  - fr
ID  - AIF_1994__44_2_559_0
ER  - 
%0 Journal Article
%A Félix, Yves
%A Thomas, Jean-Claude
%T Homologie des espaces de lacets des espaces de configuration
%J Annales de l'Institut Fourier
%D 1994
%P 559-568
%V 44
%N 2
%I Association des Annales de l’institut Fourier
%U http://archive.numdam.org/articles/10.5802/aif.1409/
%R 10.5802/aif.1409
%G fr
%F AIF_1994__44_2_559_0
Félix, Yves; Thomas, Jean-Claude. Homologie des espaces de lacets des espaces de configuration. Annales de l'Institut Fourier, Volume 44 (1994) no. 2, pp. 559-568. doi : 10.5802/aif.1409. http://archive.numdam.org/articles/10.5802/aif.1409/

[1]C.-F. Bödigheimer, F. Cohen and L. Taylor, On the homology of configuration spaces, Topology, 28 (1989), 111-123. | MR | Zbl

[2]W. Browder, Differential Hopf algebras, Trans. of the Amer. Math. Soc., 107 (1963), 153-176. | MR | Zbl

[3]R.F. Brown and J.H. White, Homology and Morse Theory of Third Configuration Spaces, Indiana University Math. Journal, 30 (1981), 501-512. | MR | Zbl

[4]F.R. Cohen, The homology of Cn+1 spaces, n ≥ 0, in F.R. Cohen, T.J. Lada and J.P. May, The homology of iterated loop spaces, Springer-Verlag, Lecture Notes in Math., 533 (1976).

[5]F.R. Cohen and L.R. Taylor, Computations of Gelfand-Fuks cohomology, the cohomology of function spaces, and the cohomology of configuration spaces, in Geometric Applications of Homotopy Theory I, Proceedings Evanston 1977, Edited by Barratt and Mahowald, Lecture Notes in Mathematics 657, Springer-Verlag (1978), 106-143. | Zbl

[6]E. Fadell and L. Neuwirth, Configuration spaces, Math. Scand., 10 (1962), 111-118. | MR | Zbl

[7]Y. Félix and S. Halperin, Rational L.S. category and its applications, Trans. Amer. Math. Soc., 273 (1982), 1-32. | MR | Zbl

[8]Y. Félix, S. Halperin and J.-C. Thomas, The Serre spectral sequence of a multiplicative fibration, preprint (1993). | Zbl

[9]Y. Félix, S. Halperin and J.-C. Thomas, Adam's cobar equivalence, Trans. Amer. Math. Soc., 329 (1992), 531-549. | MR | Zbl

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

[11]Y. Félix et D. Tanré, Sur l'homologie de l'espace des lacets d'une variété compacte, Annales Ecole Norm. Sup., 25 (1992), 617-627. | Numdam | MR | Zbl

[12]Y. Félix et J.-C. Thomas, Module d'holonomie d'une fibration, Bull. Soc. Math. France, 113 (1985), 255-258. | Numdam | MR | Zbl

[13]Y. Félix et J.-C. Thomas, Effet d'un attachement cellulaire dans l'homologie de l'espace des lacets, Annales de l'Institut Fourier, 39-1 (1989), 207-224. | Numdam | MR | Zbl

[14]S. Halperin, Lectures on minimal models, Mémoire de la Soc. Math. France, 9/10 (1983). | Numdam | MR | Zbl

[15]S. Halperin et J.-M. Lemaire, Suites inertes dans les algèbres de Lie graduées, Math. Scand., 61 (1987), 39-67. | MR | Zbl

Cited by Sources: