Geodesic
Homotopy Gerstenhaber formality of Davis–Januszkiewicz spaces
Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 325-347.

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

A homotopy Gerstenhaber structure on a differential graded algebra is essentially a family of operations defining a multiplication on its bar construction. We prove that the normalized singular cochain algebra of a Davis–Januszkiewicz space is formal as a homotopy Gerstenhaber algebra, for any coefficient ring. This generalizes a recent result by the author about classifying spaces of tori and also strengthens the well-known dga formality result for Davis–Januszkiewicz spaces due to the author and Notbohm–Ray. As an application, we determine the cohomology rings of free and based loop spaces of Davis–Januszkiewicz spaces.
DOI : 10.4310/HHA.2021.v23.n2.a17
Classification : 57Sxx, 16E45, 55P35
Keywords: Davis–Januszkiewicz space, homotopy Gerstenhaber algebra, formality, loop space 
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Matthias Franz. Homotopy Gerstenhaber formality of Davis–Januszkiewicz spaces. Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 325-347. doi : 10.4310/HHA.2021.v23.n2.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n2.a17/

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