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arXiv · 1907.04782

Homotopy Gerstenhaber formality of Davis-Januszkiewicz spaces

Matthias Franz
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Abstract

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.

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BibTeXRIS

Matthias Franz. 2019-07-10. Homotopy Gerstenhaber formality of Davis-Januszkiewicz spaces. https://doi.org/10.4310/hha.2021.v23.n2.a17

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