Topology of representation spaces of surface groups in PSL(2,R) with assigned boundary monodromy and nonzero Euler number

2016/07/15 by Gabriele Mondello, Mondello, Gabriele
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1607.04634

openalex publication_date 2016/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we complete the topological description of the space of representations of the fundamental group of a punctured surface in SL(2,R) with prescribed behavior at the punctures and nonzero Euler number, following the strategy employed by Hitchin in the unpunctured case and exploiting Hitchin-Simpson correspondence between flat bundles and Higgs bundles in the parabolic case. This extends previous results by Boden-Yokogawa and Nasatyr-Steer. A relevant portion of the paper is intended to give an overview of the subject.

Citations

• The Self-Duality Equations on a Riemann Surface

Related

• Topological components of surface group representations and signature
• Various generalizations and deformations of PSL(2,ℝ) surface group representations and their Higgs bundles
• The action of the mapping class group on representation varieties of PSL(2,R). Case I: The one-holed torus
• Connected components of the space of type-preserving representations
• Components of spaces of surface group representations