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.

EUDML-ID : urn:eudml:doc:221332
Mots clés:

@article{702134,
     title = {A proof of the Baues-Lemaire conjecture in rational homotopy theory},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1993},
     pages = {[113]-123},
     mrnumber = {MR1246625},
     zbl = {0793.55008},
     url = {http://dml.mathdoc.fr/item/702134}
}

Majewski, Martin. A proof of the Baues-Lemaire conjecture in rational homotopy theory, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1993), pp. [113]-123. http://gdmltest.u-ga.fr/item/702134/