## Opérades cellulaires et espaces de lacets itérés. (Cellular operads and iterated loop spaces.).(French)Zbl 0853.55007

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

### MSC:

 55P35 Loop spaces 20B30 Symmetric groups 06A07 Combinatorics of partially ordered sets 52B12 Special polytopes (linear programming, centrally symmetric, etc.)
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### References:

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