Connected components of Isom(\ℍ³)-representations of\n non-orientable surfaces

2021/04/30 by Juan Luis Durán Batalla, Batalla, Juan Luis Durán
Mathematics · #57M05 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2104.14880

openalex publication_date 2021/04/30 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let N_k denote the closed non-orientable surface of genus k. In this\npaper we study the behaviour of the `square map' from the group of isometries\nof hyperbolic 3-space to the subgroup of orientation preserving isometries. We\nshow that there are 2^k+1 connected components of representations of\n\π₁(N_k) in Isom(\ℍ³), which are distinguished by the\nStiefel-Whitney classes of the associated flat bundle.\n

Related

• Connected components of representation spaces of non-orientable surfaces
• Components of spaces of surface group representations
• Connected Components of The Space of Surface Group Representations
• On invariants of surfaces in the 3-sphere
• On type-preserving representations of the thrice punctured projective plane group