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A proof of the Baues-Lemaire conjecture in rational homotopy theory. (English) Zbl 0793.55008
Bureš, J. (ed.) et al., The proceedings of the 11th winter school on geometry and physics held in Srní, Czechoslovakia, January 5-12, 1991. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 30, 113-123 (1993).
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 Adams-Hilton-Anick. It is shown how this result, combined with a recent result of Anick, implies a conjecture of H. J. Baues and J. M. Lemaire [Math. Ann. 225, 219-245 (1977; Zbl 0322.55019)].
We describe in some detail the construction of these models (Section 1). We present a variant of the Adams-Hilton 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, Cenkl-Porter and Anick.
For the entire collection see [Zbl 0777.00026].

55P62 Rational homotopy theory