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Ergodicity of the mapping class group action on Deroin-Tholozan representations (2012.05775v2)
Published 10 Dec 2020 in math.DS, math.GT, and math.SG
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 $\text{PSL}(2,\mathbb{R})$, discovered by Deroin and Tholozan. We apply symplectic methods developed by Goldman and Xia to prove that the action is ergodic.
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