A canonical enriched Adams¿Hilton model for simplicial sets

• Autores: Kathryn Hess , Paul-Eugène Parent, Jonathan Scott, Andrew Tonks
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 2, 2006, págs. 847-875
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.01.013
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• Resumen

  • For any 1-reduced simplicial set K we define a canonical, coassociative coproduct on OC(K), the cobar construction applied to the normalized, integral chains on K, such that any canonical quasi-isomorphism of chain algebras from OC(K) to the normalized, integral chains on GK, the loop group of K, is a coalgebra map up to strong homotopy. Our proof relies on the operadic description of the category of chain coalgebras and of strongly homotopy coalgebra maps given in [K. Hess, P.-E. Parent, J. Scott, Bimodules over operads characterize morphisms, preprint, math.AT/0505559, 2005].