About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Majewski, Martin
A proof of the Baues-Lemaire conjecture in rational homotopy theory. (English). In: Bureš, J. and Souček, V. (eds.): Proceedings of the Winter School "Geometry and Physics". Circolo Matematico di Palermo, Palermo, 1993. pp. [113]-123
MSC: 55P62 | MR 1246625 | Zbl 0793.55008
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 Adams-Hilton-Anick. 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, 219-245 (1977; Zbl 0322.55019)].\par 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.
Partner of
EuDML logo