Opérades cellulaires et espaces de lacets itérés

Berger, Clemens

Annales de l'Institut Fourier, Tome 46 (1996), p. 1125-1157 / Harvested from Numdam

Résumé

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.

Abstract

The configuration space of $p$-tuples of pairwise distinct points in ${\bf R}^\infty $ carries a natural filtration coming from the inclusions of the ${\bf R}^n$ into ${\bf R}^\infty $. 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.

Détail

Publié le : 1996-01-01

MR 98c:55011 | MR 1415960 | Zbl 0853.55007 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.1543

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