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

Berger, Clemens

Ann. Inst. Fourier 46, No. 4, 1133-1166 (1996).

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.)

Keywords:

configuration spaces; iterated loop spaces; cellular operads; symmetric groups; permutohedra

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