论文标题
Fox-Neuwirth细胞，量子洗牌代数和B型Artin组的同源性
Fox-Neuwirth cells, quantum shuffle algebras, and the homology of type-B Artin groups
论文作者
论文摘要
在本文中，我们将从编织的矢量空间中开发出B型ARTIN组的编织代表，并与这些系数的同源性与这些系数的同源性，该系数具有特定的Bimodule在量子式支架上的同源物。作为应用，我们给出了B型Artin组的同源性的完整表征，该组在特征领域的一维辫子代表中具有系数为0。我们还将讨论该计算的两种不同方法：第一种方法扩展了由于诱导的构建构造的构造构造的构造的构造的构造，该方法扩展了辫子群的同源性的计算。 飞机。
In this paper, we will develop a family of braid representations of Artin groups of type B from braided vector spaces, and identify the homology of these groups with these coefficients with the cohomology of a specific bimodule over a quantum shuffle algebra. As an application, we give a complete characterization of the homology of type-B Artin groups with coefficients in one-dimensional braid representations over a field of characteristic 0. We will also discuss two different approaches to this computation: the first method extends a computation of the homology of braid groups due to Ellenberg-Tran-Westerland by means of induced representation, while the second method involves constructing a cellular stratification for configuration spaces of the punctured complex plane.
