no. 4
Opérades cellulaires et espaces de lacets itérés
Annales de l'Institut Fourier, Volume 46 (1996) no. 4, pp. 1125-1157.

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.

L’espace des configurations de p points distincts de R ∞ admet une filtration naturelle qui est induite par les inclusions des R n dans R ∞ . 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.

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     title = {Op\'erades cellulaires et espaces de lacets it\'er\'es},
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     volume = {46},
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Berger, Clemens. Opérades cellulaires et espaces de lacets itérés. Annales de l'Institut Fourier, Volume 46 (1996) no. 4, pp. 1125-1157. doi : 10.5802/aif.1543. https://aif.centre-mersenne.org/articles/10.5802/aif.1543/

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