Abstract
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 two 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 two-spheres or two-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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
