论文标题
lie groupoids和对数连接
Lie groupoids and logarithmic connections
论文作者
论文摘要
使用lie groupoids理论的工具，我们研究了对数$ g $捆绑的对数平面连接的类别，其中$ g $是一个复杂的还原结构组。仿射线上具有对数奇异性的平坦连接等同于与$ \ Mathbb {C} $的指示性动作相关的群体固体的表示。我们表明，这种表示允许典型的Jordan-Chevalley分解，并使用它来提供功能分类。沿着高表面的对数奇异性在复杂的歧管上的平坦连接等效于扭曲的基本型群的表示。使用Morita等效性，其构造的灵感来自Deligne具有切线底线的路径的概念，我们证明了该类别类型的范Kampen型定理。这使我们能够证明扭曲基本类固醇的表示类别可以定位于高表面的正常束。结果，我们获得了对数连接的函数riemann-hilbert对数，以广义单构型数据来获得。
Using tools from the theory of Lie groupoids, we study the category of logarithmic flat connections on principal $G$-bundles, where $G$ is a complex reductive structure group. Flat connections on the affine line with a logarithmic singularity at the origin are equivalent to representations of a groupoid associated to the exponentiated action of $\mathbb{C}$. We show that such representations admit a canonical Jordan-Chevalley decomposition and use this to give a functorial classification. Flat connections on a complex manifold with logarithmic singularities along a hypersurface are equivalent to representations of a twisted fundamental groupoid. Using a Morita equivalence, whose construction is inspired by Deligne's notion of paths with tangential basepoints, we prove a van Kampen type theorem for this groupoid. This allows us to show that the category of representations of the twisted fundamental groupoid can be localized to the normal bundle of the hypersurface. As a result, we obtain a functorial Riemann-Hilbert correspondence for logarithmic connections in terms of generalized monodromy data.
