The configuration space of -tuples of pairwise distinct points in carries a natural filtration coming from the inclusions of the into . 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 -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 points distincts de admet une filtration naturelle qui est induite par les inclusions des dans . 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 -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}, pages = {1125--1157}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {4}, year = {1996}, doi = {10.5802/aif.1543}, zbl = {0853.55007}, mrnumber = {1415960}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.1543/} }
TY - JOUR AU - Berger, Clemens TI - Opérades cellulaires et espaces de lacets itérés JO - Annales de l'Institut Fourier PY - 1996 SP - 1125 EP - 1157 VL - 46 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1543/ DO - 10.5802/aif.1543 LA - fr ID - AIF_1996__46_4_1125_0 ER -
%0 Journal Article %A Berger, Clemens %T Opérades cellulaires et espaces de lacets itérés %J Annales de l'Institut Fourier %D 1996 %P 1125-1157 %V 46 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1543/ %R 10.5802/aif.1543 %G fr %F 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/articles/10.5802/aif.1543/
[1] Iterated monoidal categories, preprint (1995).
, , et ,[2] Geometry of loop spaces and the cobar-construction, Mem. of the Amer. Math. Soc., 230 (1980). | MR | Zbl
,[3] Γ+-Structures I, II, III, Topology, 13 (1974), 25-45, 113-126, 199-207. | Zbl
et ,[4] Un groupoïde simplicial comme modèle de l'espace des chemins, Bull. Soc. Math. France, 123 (1995), 1-32. | Numdam | MR | Zbl
,[5] On puzzles and polytope isomorphism, Aequationes Math., 34 (1987), 287-297. | MR | Zbl
et ,[6] Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Math. 347, Springer Verlag (1973). | MR | Zbl
et ,[7] The homology of Cn+1-spaces, Lecture Notes in Math. 533, Springer Verlag (1976), 207-351. | MR | Zbl
,[8] Splitting of certain spaces CX, Math. Proc. Camb. Phil. Soc., 84 (1978), 465-496. | MR | Zbl
, et ,[9] Tensor product of operads and iterated loop spaces, Journal of Pure and Applied Algebra, 50 (1988), 237-258. | MR | Zbl
,[10] The braid groups, Math. Scand., 10 (1962), 119-126. | MR | Zbl
et ,[11] The permutoassociahedron, MacLane's coherence theorem and asymptotic zones for KZ equation, Journal of Pure and Applied Algebra, 85 (1993), 119-142. | Zbl
,[12] On the Homotopy Type of Configuration Complexes, Contemporary Math., 146 (1993), 159-170. | MR | Zbl
,[13] The Geometry of iterated loop spaces, Lecture Notes in Math., 277, Springer Verlag (1972). | MR | Zbl
,[14] E∞-spaces, group completions and permutative categories, London Math. Soc. Lecture Notes, 11 (1974), 61-94. | Zbl
,[15] Iterated loop spaces, Annals of Math., 84 (1966), 386-403. | MR | Zbl
,[16] Higher algebraic K-theory I, Lecture Notes in Math., 341, Springer Verlag (1973), 85-147. | MR | Zbl
,[17] Configuration spaces and iterated loop spaces, Inventiones Math., 21 (1973), 213-221. | MR | Zbl
,[18] Simplicial Group Models for ΩnSnX, Israel Journal of Math., 66 (1989), 330-350. | MR | Zbl
,Cited by Sources: