Opérades cellulaires et espaces de lacets itérés

Clemens Berger

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 4, page 1125-1157
  • ISSN: 0373-0956

Abstract

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The configuration space of p -tuples of pairwise distinct points in R ∞ carries a natural filtration coming from the inclusions of the R n into R ∞ . We characterize the homotopy type of this filtration by the combinatorial properties of an underlying cellular structure and establish a close relationship to May’s theory of E n -operads. This gives a unified approach to the different known combinatorial models of iterated loop spaces reproving by the way the approximation theorems of Milgram, Smith and Kashiwabara.

How to cite

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Berger, Clemens. "Opérades cellulaires et espaces de lacets itérés." Annales de l'institut Fourier 46.4 (1996): 1125-1157. <http://eudml.org/doc/75202>.

@article{Berger1996,
abstract = {L’espace des configurations de $p$ points distincts de $\{\bf R\}^\infty $ admet une filtration naturelle qui est induite par les inclusions des $\{\bf R\}^n$ dans $\{\bf R\}^\infty $. Nous caractérisons le type d’homotopie de cette filtration par les propriétés combinatoires d’une structure cellulaire sous-jacente, étroitement liée à la théorie des $E_n$-opérades de May. Cela donne une approche unifiée des différents modèles combinatoires d’espaces de lacets itérés et redémontre les théorèmes d’approximation de Milgram, Smith et Kashiwabara.},
author = {Berger, Clemens},
journal = {Annales de l'institut Fourier},
keywords = {configuration spaces; iterated loop spaces; cellular operads; symmetric groups; permutohedra},
language = {fre},
number = {4},
pages = {1125-1157},
publisher = {Association des Annales de l'Institut Fourier},
title = {Opérades cellulaires et espaces de lacets itérés},
url = {http://eudml.org/doc/75202},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Berger, Clemens
TI - Opérades cellulaires et espaces de lacets itérés
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 4
SP - 1125
EP - 1157
AB - L’espace des configurations de $p$ points distincts de ${\bf R}^\infty $ admet une filtration naturelle qui est induite par les inclusions des ${\bf R}^n$ dans ${\bf R}^\infty $. Nous caractérisons le type d’homotopie de cette filtration par les propriétés combinatoires d’une structure cellulaire sous-jacente, étroitement liée à la théorie des $E_n$-opérades de May. Cela donne une approche unifiée des différents modèles combinatoires d’espaces de lacets itérés et redémontre les théorèmes d’approximation de Milgram, Smith et Kashiwabara.
LA - fre
KW - configuration spaces; iterated loop spaces; cellular operads; symmetric groups; permutohedra
UR - http://eudml.org/doc/75202
ER -

References

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