论文标题
扭曲的当地野生地图课程组：配置空间，裂变树和复杂的辫子
Twisted local wild mapping class groups: configuration spaces, fission trees and complex braids
论文作者
论文摘要
在完成代数构建泊松野生角色品种（b。-Yamakawa，2015）之后，人们可以考虑它们的自然变形，从而推广出对常规（TAME）角色品种的映射类组动作，又概括了已经在野生/违规环境中出现的G-Braid群体。在这里，我们研究了这些野生映射的班级组。正如我们所记得的那样，根据野生黎曼表面的可接受变形，这个故事是最自然的。主要结果是：1）构造包含所有可能局部变形的配置空间，2）组合物体的定义，即任何野生riemann表面的``裂变林''的定义，并证明了它给出了所有可允许的变形类别的尖锐参数化。作为1）的应用，通过考虑基本示例，我们表明所有复杂反射组的编织组称为广义对称组，似乎是野生地图类别组。作为2）的应用，我们计算了A型A型野生riemann表面的所有（全局）模量空间（在固定的可允许变形类中），这是对紧凑型Riemann Riemann表面模量空间的著名``riemann's count''的概括。
Following the completion of the algebraic construction of the Poisson wild character varieties (B.--Yamakawa, 2015) one can consider their natural deformations, generalising both the mapping class group actions on the usual (tame) character varieties, and the G-braid groups already known to occur in the wild/irregular setting. Here we study these wild mapping class groups in the case of arbitrary formal structure in type A. As we will recall, this story is most naturally phrased in terms of admissible deformations of wild Riemann surfaces. The main results are: 1) the construction of configuration spaces containing all possible local deformations, 2) the definition of a combinatorial object, the ``fission forest'', of any wild Riemann surface and a proof that it gives a sharp parameterisation of all the admissible deformation classes. As an application of 1), by considering basic examples, we show that the braid groups of all the complex reflection groups known as the generalised symmetric groups appear as wild mapping class groups. As an application of 2), we compute the dimensions of all the (global) moduli spaces of type A wild Riemann surfaces (in fixed admissible deformation classes), a generalisation of the famous ``Riemann's count'' of the dimensions of the moduli spaces of compact Riemann surfaces.
