Connected components of representation spaces of non-orientable surfaces

2009/09/13 by Frédéric Palesi, Palesi, Frederic
Mathematics · #57M05 #57R20 #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.0909.2421

openalex publication_date 2009/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a compact closed non-orientable surface. We show that the space of representations of the fundamental group of M into PSL(2,R) has exactly two connected components. These two components are the preimages of a certain Stiefel-Whitney characteristic class, computed in a similar way as the Euler class in the orientable case.

Citations

• The space of surface group representations

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