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arXiv · 1910.08455

Adams' cobar construction revisited

Manuel Rivera
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Abstract

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.

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Manuel Rivera. 2019-10-18. Adams' cobar construction revisited. https://arxiv.org/abs/1910.08455

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