Mapping class group orbit closures for Deroin-Tholozan representations

TL;DR

This paper demonstrates that the mapping class group acts densely on the character variety of Deroin-Tholozan representations, highlighting the minimality of the action except for finite orbits, through symplectic geometric methods.

Contribution

It establishes the density of infinite orbits in the character variety, providing a geometric perspective on the dynamics of the mapping class group action.

Findings

Infinite mapping class group orbits are dense in the character variety.

The action of the mapping class group is minimal except for finite orbits.

Symplectic structure is key to the proof.

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.