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A classical E-infinity operad is formed by the bar construction of thesymmetric groups. Such an operad has been introduced by M. Barratt and P.Eccles in the context of simplicial sets in order to have an analogue of theMilnor FK-construction for infinite loop spaces. The purpose of this article isto prove that the associative algebra structure on the normalized cochaincomplex of a simplicial set extends to the structure of an algebra over theBarratt-Eccles operad. We also prove that differential graded algebras over theBarratt-Eccles operad form a closed model category. Similar results hold forthe normalized Hochschild cochain complex of an associative algebra. Moreprecisely, the Hochschild cochain complex is acted on by a suboperad of theBarratt-Eccles operad which is equivalent to the classical little squaresoperad.Comment: 46 pages. Final versio

Combinatorial operad actions on cochains