Summary:

This paper contains an announcement of a result, which settles the connection between various algebraic models for rational homotopy theory: the models of Quillen, Sullivan and AdamsHiltonAnick. It is shown how this result, combined with a recent result of Anick, implies a conjecture of {\it H. J. Baues} and {\it J. M. Lemaire} [Math. Ann. 225, 219245 (1977; Zbl 0322.55019)].\par We describe in some detail the construction of these models (Section 1). We present a variant of the AdamsHilton model, which is defined in a natural way for simplicial sets. A forthcoming paper will contain a detailed proof of Theorem 1. A generalization to mild homotopy theories is in preparation, where we establish a close connection between extensions of the rational theories due to Dwyer, CenklPorter and Anick. (English) 