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.
@article{urn:eudml:doc:41699,
title = {Exploring W.G. Dwyer's tame homotopy theory.},
journal = {Publicacions Matem\`atiques},
volume = {35},
year = {1991},
pages = {375-402},
mrnumber = {MR1201563},
zbl = {0742.55006},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41699}
}
Scheerer, Hans; Tanré, Daniel. Exploring W.G. Dwyer's tame homotopy theory.. Publicacions Matemàtiques, Tome 35 (1991) pp. 375-402. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41699/