论文标题
$ \ mathrm {sl} _2（\ mathbb {c}）$的兼容裤子分解
Compatible pants decompositions for $\mathrm{SL}_2(\mathbb{C})$-representations of surface groups
论文作者
论文摘要
对于将表面组的任何不可约定表示为$ \ mathrm {sl} _2（\ mathbb {c}）$，我们表明存在一个裤子分解，其中对任何一对裤子的限制是不可修复的，而分解的曲线无需发送到跟踪$ \ pm pm 2 $ element。我们证明了$ \ mathrm {so} _3 $ -presentations的类似属性。我们还调查了在此设置中可能发生的给定表示形式的裤子分解类型。这一结果是在先前的第一和第三名作者的论文中宣布的，该论文是由统一根部的Skein代数的Azumaya基因座进行的。
For any irreducible representation of a surface group into $\mathrm{SL}_2(\mathbb{C})$, we show that there exists a pants decomposition where the restriction to any pair of pants is irreducible and where no curve of the decomposition is sent to a trace $\pm 2$ element. We prove a similar property for $\mathrm{SO}_3$-representations. We also investigate the type of pants decomposition that can occur in this setting for a given representation. This result was announced in a previous paper of the first and third named authors, motivated by the study of the Azumaya locus of the skein algebra of surfaces at roots of unity.
