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Title: A proof of the Baues-Lemaire conjecture in rational homotopy theory (English)
Author: Majewski, Martin
Language: English
Journal: Proceedings of the Winter School "Geometry and Physics"
Issue: 1991
Pages: [113]-123
Category: math
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. (English)
MSC: 55P62
idZBL: Zbl 0793.55008
idMR: MR1246625
Date available: 2009-07-18T21:12:04Z
Last updated: 2012-09-18
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