Homologie des espaces de lacets des espaces de configuration

Yves Félix; Jean-Claude Thomas

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 2, page 559-568
  • ISSN: 0373-0956

Abstract

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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 , ℚ ) is not generated by one generator, then the rational homology of Ω F ( M , k ) contains a tensor algebra for k ≥ 2 .

How to cite

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Félix, Yves, and Thomas, Jean-Claude. "Homologie des espaces de lacets des espaces de configuration." Annales de l'institut Fourier 44.2 (1994): 559-568. <http://eudml.org/doc/75073>.

@article{Félix1994,
abstract = {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 $M$.},
author = {Félix, Yves, Thomas, Jean-Claude},
journal = {Annales de l'institut Fourier},
keywords = {homology of loop spaces of configuration spaces of simply connected manifolds},
language = {fre},
number = {2},
pages = {559-568},
publisher = {Association des Annales de l'Institut Fourier},
title = {Homologie des espaces de lacets des espaces de configuration},
url = {http://eudml.org/doc/75073},
volume = {44},
year = {1994},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 2
SP - 559
EP - 568
AB - 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 $M$.
LA - fre
KW - homology of loop spaces of configuration spaces of simply connected manifolds
UR - http://eudml.org/doc/75073
ER -

References

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  4. [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). Zbl0334.55009
  5. [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. Zbl0398.55004
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  8. [8]Y. FÉLIX, S. HALPERIN and J.-C. THOMAS, The Serre spectral sequence of a multiplicative fibration, preprint (1993). Zbl0978.55012
  9. [9]Y. FÉLIX, S. HALPERIN and J.-C. THOMAS, Adam's cobar equivalence, Trans. Amer. Math. Soc., 329 (1992), 531-549. Zbl0765.55005MR92e:55007
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  11. [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. Zbl0774.57021MR93m:55019
  12. [12]Y. FÉLIX et J.-C. THOMAS, Module d'holonomie d'une fibration, Bull. Soc. Math. France, 113 (1985), 255-258. Zbl0587.55007MR87i:55022
  13. [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. Zbl0686.55005MR90j:55012
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