CELLULAR OPERADS AND ITERATED LOOP-SPACES

The configuration space of p-tuples of pairwise distinct points in R(i nfinity) carries a natural filtration coming from the inclusions of th e R(n) into R(infinity). We characterize the homotopy type of this fil tration by the combinatorial properties of an underlying cellular stru cture and establish a close relationship to May's theory of E(n)-opera ds. This gives a unified approach to the different known combinatorial models of iterated loop spaces reproving by the way the approximation theorems of Mile;ram, Smith and Kashiwabara.