Ergodicity of the mapping class group action on Deroin-Tholozan representations

2020/12/10 by Arnaud Maret, Maret, Arnaud
Mathematics · #57M05 #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2012.05775

openalex publication_date 2020/12/10 · openalex created_date 2022/10/14 · openalex updated_date 2026/07/28

Abstract

This note investigates the dynamics of the mapping class group action on the character variety of super-maximal representations of the fundamental group of a punctured sphere into PSL(2,ℝ), discovered by Deroin and Tholozan. We apply symplectic methods developed by Goldman and Xia to prove that the action is ergodic.

Related

• Mapping class group orbit closures for Deroin-Tholozan representations
• The action of the mapping class group on representation varieties of PSL(2,R). Case I: The one-holed torus
• The modular action on PSL2(R)-characters in genus 2
• Ergodicity of Mapping Class Group Actions on Representation Varieties, I. Closed Surfaces
• Mapping class group dynamics on Aff(C)-characters