Exploring W.G. Dwyer's tame homotopy theory.

Título inglés Exploring W.G. Dwyer's tame homotopy theory.
Título español Exploración de la teoría de homotopía de W.G. Dwyer.
Autor/es Scheerer, Hans ; Tanré, Daniel
Organización Math. Inst. FU Berlin II, Berlín, Alemania;Univ. Sci. Tech. Lille Flandres Artois, Villeneuve d'Ascq, Francia
Revista 0214-1493
Publicación 1991, 35 (2): 375-402, 22 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Let Sr be the category of r-reduced simplicial sets, r ≥ 3; let Lr-1 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 Sr is equivalent to the associated homotopy category of Lr-1. Here we embark on a study of this equivalence and its implications. In particular, we show how to compute homology, cohomology, homotopy with coefficients and Whitehead products (in the tame range) of a simplicial set out of the corresponding Lie algebra. Furthermore we give an application (suggested by E. Vogt) to π*(BΓ3) where BΓ3 denotes the classifying space of foliations of codimension 3.
Código MathReviews MR1201563
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