Davis-Januszkiewicz空间的同伦Gerstenhaber形式
Homotopy Gerstenhaber formality of Davis-Januszkiewicz spaces
摘要：
微分分次代数上的同伦Gerstenhaber结构本质上是定义其条结构上的乘法的一族运算。证明了Davis-Januszkiewicz空间的正规奇异上链代数对于任何系数环都是同伦Gerstenhaber代数.这推广了作者最近关于环面空间分类的一个结果，也加强了作者和Notbohm-Ray关于Davis-Januszkiewicz空间的著名dga形式结果。作为应用，我们确定了Davis-Januszkiewicz空间的自由和基闭路空间的上同调环.
英文摘要：
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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