Geodesic
$E_{\infty}$ obstruction theory
Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 155-184.

Voir la notice de l'article provenant de la source International Press of Boston

The space of $E_{\infty}$ structures on a simplicial operad $\mathcal{C}$ is the limit of a tower of fibrations, so its homotopy is the abutment of a Bousfield–Kan fringed spectral sequence. The spectral sequence begins (under mild restrictions) with the stable cohomotopy of the right $\Gamma$-module $\pi_{*} \mathcal{C}$; the fringe contains an obstruction theory for the existence of $E_{\infty}$ structures on $\mathcal{C}$. This formulation is very flexible: applications extend beyond structures on classical ring spectra to examples in motivic homotopy theory.
DOI : 10.4310/HHA.2018.v20.n1.a10
Classification : 18D50, 55P43, 55P48, 55S35
Keywords: operad, $E_{\infty}$ structure, Bousfield–Kan spectral sequence 
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Alan Robinson. $E_{\infty}$ obstruction theory. Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 155-184. doi : 10.4310/HHA.2018.v20.n1.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n1.a10/

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