论文标题
相干分析式滑轮的简单Chern-Weil理论，第二部分
Simplicial Chern-Weil theory for coherent analytic sheaves, part II
论文作者
论文摘要
在此Diptych的前部分中，我们定义了可接受的简单连接的概念，并解释了H.I.绿色构建了通过本地无皮带轮在čech神经上的一致分析带的分辨率。本文旨在通过表明格林的重心简单连接确实可以接受这些抽象的形式主义，并且这种情况正是我们所需要的，以便能够应用Chern-Weil理论并构建特征类别。我们表明，在（全球）向量捆绑包的情况下，简单的构造与可以手动构建的内容一致：矢量捆绑包的指数atiyah类的显式čech代表同意。最后，我们总结了所有上述理论如何符合在一起的方式，以使我们能够定义Chern类别的相干分析或骨的类别，并在紧凑型情况下显示出独特性。
In the previous part of this diptych, we defined the notion of an admissible simplicial connection, as well as explaining how H.I. Green constructed a resolution of coherent analytic sheaves by locally free sheaves on the Čech nerve. This paper seeks to apply these abstract formalisms, by showing that Green's barycentric simplicial connection is indeed admissible, and that this condition is exactly what we need in order to be able to apply Chern-Weil theory and construct characteristic classes. We show that, in the case of (global) vector bundles, the simplicial construction agrees with what one might construct manually: the explicit Čech representatives of the exponential Atiyah classes of a vector bundle agree. Finally, we summarise how all the preceding theory fits together to allow us to define Chern classes of coherent analytic sheaves, as well as showing uniqueness in the compact case.
