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 |
Acceso al artículo completo |