亏格为2的闭曲面的基本群的SO（3）- character空间的两个分支
The two components of the SO(3)-character space of the fundamental group of a closed surface of genus 2
摘要：
利用几何技巧，通过SO（3）的共轭作用，明确地找到亏格为2的闭曲面的基本群的SO（3）-表示空间的拓扑结构.空间有两个组成部分。我们将描述这两个分量的拓扑，并通过用球面三角形参数化它们来描述相应的SU（2）-特征空间。每个分支都有16对1的分支覆盖，分支轨迹是2-球面或2-环面的并集。在此过程中，我们还描述了这两个空间的拓扑结构。稍后我们将把这个结果与将来的工作联系起来，研究更高亏格的情况和SL（3，R）-表示。
英文摘要：
We use geometric techniques to explicitly find the topological structure of the space of SO(3)-representations of the fundamental group of a closed surface of genus 2 quotient by the conjugation action by SO(3). There are two components of the space. We will describe the topology of both components and describe the corresponding SU(2)-character spaces by parametrizing them by spherical triangles. There is the sixteen to one branch-covering for each component, and the branch locus is a union of 2-spheres or 2-tori. Along the way, we also describe the topology of both spaces. We will later relate this result to future work into higher-genus cases and the SL(3,R)-representations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
