Opérades cellulaires et espaces de lacets itérés
Annales de l'Institut Fourier, Volume 46 (1996) no. 4, p. 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.
@article{AIF_1996__46_4_1125_0,
     author = {Berger, Clemens},
     title = {Op\'erades cellulaires et espaces de lacets it\'er\'es},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {46},
     number = {4},
     year = {1996},
     pages = {1125-1157},
     doi = {10.5802/aif.1543},
     mrnumber = {1415960},
     zbl = {0853.55007},
     mrnumber = {98c:55011},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1996__46_4_1125_0}
}
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. http://www.numdam.org/item/AIF_1996__46_4_1125_0/

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