Non-commutative Hodge structures: Towards matching categorical and geometric examples
Non-commutative Hodge structures: Towards matching categorical and geometric examples
复制标题
非交换霍奇结构：面向匹配分类和几何示例
DOI：
10.1090/s0002-9947-2014-05913-8
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发表时间：
2011
影响因子：
1.3
通讯作者：
D. Shklyarov
中科院分区：
文献类型：
--
作者：
D. Shklyarov
本文研究微分分次代数和范畴的周期循环同调上的非交换Hodge结构的de Rham部分。我们讨论了在穿孔形式圆盘上的周期循环同调丛上相应联络的显式公式。我们的主要结果说，一类多项式的矩阵因式分解的公式再现，到一定的转变，一个众所周知的连接相关的扭曲德拉姆上同调起着核心作用的几何方法霍奇理论的孤立奇点。
The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the periodic cyclic homology viewed as a bundle over the punctured formal disk. Our main result says that for the category of matrix factorizations of a polynomial the formulas reproduce, up to a certain shift, a well-known connection on the associated twisted de Rham cohomology which plays a central role in the geometric approach to the Hodge theory of isolated singularities.