Homotopy Gerstenhaber formality of Davis-Januszkiewicz spaces
Algebraic Topology
2021-08-31 v3
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.
Keywords
Cite
@article{arxiv.1907.04782,
title = {Homotopy Gerstenhaber formality of Davis-Januszkiewicz spaces},
author = {Matthias Franz},
journal= {arXiv preprint arXiv:1907.04782},
year = {2021}
}
Comments
22 pages; conventions in Section 2.7 clarified, new Remark 3.2, minor changes