Parametrization of PSL (2, C) -representations of surface groups
Parametrization of PSL (2, C) -representations of surface groups
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PSL (2, C) 的参数化 - 表面基团的表示
DOI：
10.1007/s10711-013-9866-x
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发表时间：
2014
影响因子：
0.5
通讯作者：
Yuichi Kabaya
中科院分区：
文献类型：
--
作者：
Ryoyo Ikebuchi;Satoru Konnai;Yuji Sunden;Shiro Murata;Misao Onuma;Kazuhiko Ohashi;池渕良洋;Yuichi Kabaya
对于具有边界分量的亏格的定向曲面，我们构造了一个有理映射，该映射是从的子集到的特征簇的开代数子集的有理映射，作为Fenchel-Nielsen坐标的一个模拟。在有限群的作用下取商之后，我们得到了特征簇的子集的参数化，对于特征簇也是如此。利用参数的有理函数可以系统地计算出一组矩阵生成元。给出了裤子分解的初等移动下的变换公式。
For an oriented surface of genuswithboundary components, we construct a rational map from a subset ofonto an open algebraic subset of the-character variety as an analogue of the Fenchel-Nielsen coordinates. After taking the quotient by an action of a finite group, we obtain a parametrization of a subset of the-character variety, and similarly for the-character variety. We can systematically calculate a set of matrix generators by rational functions of the parameters. We give transformation formulae under elementary moves of pants decompositions.