A canonical enriched Adams-Hilton model for simplicial sets

Abstract

For any 1-reduced simplicial set $K$ we define a canonical, coassociative coproduct on \Om C(K), the cobar construction applied to the normalized, integral chains on $K$, such that any canonical quasi-isomorphism of chain algebras from \Om C(K) to the normalized, integral chains on $GK$, the loop group of $K$, is a coalgebra map up to strong homotopy. Our proof relies on the operadic description of the category of chain coalgebras and of strongly homotopy coalgebra maps given in math.AT/0505559.Comment: 28 pages. This revised version incorporates operadic techniques developed in math.AT/050555