The geometry of the mapping class group action on the character variety of surface groups

研究了一次穿透环面的SL(2，C)特征变化。特别地，我们研究了由Bowditch产生的Q-条件、相应表示的离散性、映射类群操作对字符种类的动态复杂性之间的关系。我们与小森洋平联合发表了一篇关于字符种类的线性切片的离散轨迹的全局结构的论文。我们对Minsky最近提出的本原稳定性进行了计算机实验，测量了映射类群作用动力学的复杂性，并与Q-条件进行了比较。

We studied the SL(2,C)-character variety of once punctured torus. In particular, we investigate the relation between the Q-condition due to Bowditch, the discreteness of the corresponding representation, the complexity of the dynamics of the mapping class group action on the character variety. We published a joint paper with Yohei Komori on the global structure of the discreteness loci of the linear slices of the character variety. We carried our a computer experiments on primitive stableness, which was introduced recently by Minsky and measures the complexity of the dynamics of the mapping class group action, and compared our results with Q-condition.