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

Publicacions Matemàtiques (1991)

- Volume: 35, Issue: 2, page 375-402
- ISSN: 0214-1493

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topScheerer, 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 -