Mapping class group orbit closures for Deroin-Tholozan representations

2024/11/15 by Bouilly, Yohann, Faraco, Gianluca, Maret, Arnaud
#20C15 #37B05 #57K20 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2411.10269

Abstract

We prove that infinite mapping class group orbits are dense in the character variety of Deroin-Tholozan representations. In other words, the action is minimal except for finite orbits. Our arguments rely on the symplectic structure of the character variety, emphasizing this geometric perspective over its algebraic properties.

Related

• Tykhyy's Conjecture on finite mapping class group orbits
• Ergodicity of the mapping class group action on Deroin-Tholozan representations
• Modular orbits on the representation spaces of compact abelian Lie groups
• The orbit method for profinite groups and a p-adic analogue of Brown's theorem
• Well displacing representations and orbit maps