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

Scheerer, Hans, and Tanré, Daniel. "Exploring W.G. Dwyer's tame homotopy theory.." Publicacions Matemàtiques 35.2 (1991): 375-402. <http://eudml.org/doc/41699>.

@article{Scheerer1991,
abstract = {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.},
author = {Scheerer, Hans, Tanré, Daniel},
journal = {Publicacions Matemàtiques},
keywords = {tame homotopy category; simplicial sets; differential graded Lie algebras; Whitehead products},
language = {eng},
number = {2},
pages = {375-402},
title = {Exploring W.G. Dwyer's tame homotopy theory.},
url = {http://eudml.org/doc/41699},
volume = {35},
year = {1991},
}

TY - JOUR
AU - Scheerer, Hans
AU - Tanré, Daniel
TI - Exploring W.G. Dwyer's tame homotopy theory.
JO - Publicacions Matemàtiques
PY - 1991
VL - 35
IS - 2
SP - 375
EP - 402
AB - 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.
LA - eng
KW - tame homotopy category; simplicial sets; differential graded Lie algebras; Whitehead products
UR - http://eudml.org/doc/41699
ER -