论文标题
Gelfand-Fuks共同体的局部到全球分析
A local-to-global analysis of Gelfand-Fuks cohomology
论文作者
论文摘要
我们提出了一种新颖的证明技术，用于在平滑的歧管上构造矢量频场的对角线雪瓦利 - 埃伦贝格共同体，从而通过平滑的歧管进行了媒介领域，并通过从分量代数和cosheaves的理论中对局部到全球的分析进行了局部到全球分析。这种方法产生了一种统一的方法来处理在歧管的不同笛卡尔力量上比较“类似捆的”数据的问题，并且很容易将其推广到研究与几何学对象相关的其他同胞理论的研究。独立地，我们对正式矢量领域和欧几里得空间上的矢量领域和矢量领域的连续Chevalley-Eilenberg共同介绍了一个详细且易于访问的博览会，现代化并阐述了Bott，Fun和Gelfand对主题的知名文献。
We present a novel proof technique to construct the Gelfand-Fuks spectral sequence for diagonal Chevalley-Eilenberg cohomology of vector fields on a smooth manifold, performing a local-to-global analysis through a notion of generalized good covers from the theory of factorization algebras and cosheaves. This approach yields a unified way to deal with the problem of comparing "sheaf-like" data over different Cartesian powers of the manifold, and is easily generalized to the study of other cohomology theories associated to geometric objects. Independently, we lay out a detailed and easily accessible exposition on the continuous Chevalley-Eilenberg cohomology of formal vector fields and of vector fields on Euclidean space, modernizing and elaborating on well-established literature on the subject by Bott, Fuks, and Gelfand.
