2010/02/28 by Suhyoung Choi, SUHYOUNG CHOI
Mathematics · #Advanced Algebra and Geometry #Fundamental group #Geometric and Algebraic Topology #Group (periodic table) #Group action #Homotopy and Cohomology in Algebraic Topology #Locus (genetics) #Quotient #Quotient space (topology) #Surface (topology) #Topology (electrical circuits) #math.GN #math.GR #math.GT #msc:57M50
paper · pdf · doi:10.1142/s0129167x11007185
published as Int. J. Mathematics, Vol 22. no. 9 pp. 1261-1364 (2011)
arxiv created 2010/09/02 · openalex publication_date 2011/03/14 · arxiv updated 2016/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.