Caldararu猜想与Tsygan形式
Caldararu's conjecture and Tsygan's formality
摘要：
本文完成了Caldararu关于多向量场上微分形式模结构相容性和Hochschild上同调霍赫希尔德同调猜想的证明。事实上，我们表明，扭曲的平方根的托德类给出了同构的precalculi之间的这些对对象。我们的方法使用形式几何全球化的Kontsevich和Shoikhet（后者的存在是由Tsygan证明）介绍的地方形式准同构。我们还依赖于一个事实-最近证明的前两个作者-Shoikhet的准同构是兼容的卡积扭曲后的Maurer-Cartan元素。
英文摘要：
In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over poly-vector fields and on Hochschild homology over Hochschild cohomology. In fact we show that twisting with the square root of the Todd class gives an isomorphism of precalculi between these pairs of objects. Our methods use formal geometry to globalize the local formality quasi-isomorphisms introduced by Kontsevich and Shoikhet (the existence of the latter was conjectured by Tsygan). We also rely on the fact - recently proved by the first two authors - that Shoikhet's quasi-isomorphism is compatible with cap product after twisting with a Maurer-Cartan element.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
