论文标题
当地的野生地图课程组和有线辫子
Local wild mapping class groups and cabled braids
论文作者
论文摘要
我们将定义和研究纯$ \ mathfrak {g} $ - 曲线理论中发生的纯$ \ mathfrak {g} $ - 辫子组，对于任何复杂的还原性谎言代数$ \ mathfrak {g} $。它们构成了野生地图课程组的本地部分，它们是野生黎曼表面（普遍）变形的基本组，其基础是Stokes数据的编织，并推广了通常的映射课程组。我们将为当地的野生地图类别组建立一般产品分解，在许多情况下，定义了控制这种分解的裂变树。进一步在A型中，我们将显示一个与辫子作战有关的辫子组的有线版本。
We will define and study some generalisations of pure $\mathfrak{g}$-braid groups that occur in the theory of connections on curves, for any complex reductive Lie algebra $\mathfrak{g}$. They make up local pieces of the wild mapping class groups, which are fundamental groups of (universal) deformations of wild Riemann surfaces, underlying the braiding of Stokes data and generalising the usual mapping class groups. We will establish a general product decomposition for the local wild mapping class groups, and in many cases define a fission tree controlling this decomposition. Further in type A we will show one obtains cabled versions of braid groups, related to braid operads.
