Geodesic
Adams' cobar construction revisited
Documenta mathematica, Tome 27 (2022), pp. 1213-1223.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We give a short and streamlined proof of the following statement recently proven by the author and M. Zeinalian: the cobar construction of the dg coassociative coalgebra of normalized singular chains on a path-connected pointed space is naturally quasi-isomorphic as a dg associative algebra to the singular chains on the based loop space. This extends a classical theorem of F. Adams originally proven for simply connected spaces. Our proof is based on relating the cobar functor to the left adjoint of the homotopy coherent nerve functor.
Classification : 57T30, 55P35, 57T25
Keywords: cobar construction, based loop space, homotopy coherent nerve 
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     author = {Rivera, Manuel},
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Rivera, Manuel. Adams' cobar construction revisited. Documenta mathematica, Tome 27 (2022), pp. 1213-1223. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a36/