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Michael A. Mandell (2006)
Publications Mathématiques de l'IHÉS
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Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E algebras is faithful but not full.
Timothy Porter (1978)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Levine, Marc (2007)
Documenta Mathematica
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Majewski, Martin
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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 and [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...
Hans Scheerer, Daniel Tanré (1991)
Publicacions Matemàtiques
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Let S be the category of r-reduced simplicial sets, r ≥ 3; let L be the category of (r-1)-reduced differential graded Lie algebras over Z. According to the fundamental work [3] of W.G. Dwyer both categories are endowed with closed model category structures such that the associated tame homotopy category of S is equivalent to the associated homotopy category of L. Here we embark on a study of this equivalence and its implications. In particular, we show how to compute homology, cohomology,...
Flores , Ramón J. (2005)
Algebraic & Geometric Topology
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J. G. Cabello (1997)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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