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arXiv · 1001.4650

Koszul duality complexes for the cohomology of iterated loop spaces of spheres

Benoit Fresse
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Abstract

The goal of this article is to make explicit a structured complex whose homology computes the cohomology of the p-profinite completion of the n-fold loop space of a sphere of dimension d=n-m<n. This complex is defined purely algebraically, in terms of characteristic structures of E_n-operads. Our construction involves: the free complete algebra in one variable associated to any E_n-operad; and an element in this free complete algebra, which is associated to a morphism from the operad of L-infinity algebras to an operadic suspension of our E_n-operad. We deduce our main theorem from: a connection between the cohomology of iterated loop spaces and the cohomology of algebras over E_n-operads; and a Koszul duality result for E_n-operads.

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Benoit Fresse. 2010-01-26. Koszul duality complexes for the cohomology of iterated loop spaces of spheres. https://doi.org/10.1090/conm%2F617

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