Exploring W.G. Dwyer's tame homotopy theory

• Autores: Hans Scheerer, Daniel Tanré
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 35, Nº 2, 1991, págs. 375-402
• Idioma: inglés
• DOI: 10.5565/publmat_35291_05
• Títulos paralelos:
  • Exploración de la teoría de homotopía de W.G. Dwyer
• Enlaces
  • Texto completo
• Resumen

  • 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 p*(BG3) where BG3 denotes the classifying space of foliations of codimension 3.