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arXiv · 2605.02823

Invariant measures for Deroin-Tholozan representations

Yohann Bouilly·Arnaud Maret
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Abstract

We classify mapping class group invariant probability measures on the character varieties of Deroin-Tholozan representations, namely the compact components of relative $\mathrm{PSL}_2\mathbb{R}$-character varieties. We prove that an ergodic measure is either the counting measure on a finite orbit or agrees with the Liouville measure induced by the Goldman symplectic form. Our approach is based on measure disintegration along transverse Lagrangian tori fibrations.

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Yohann Bouilly, Arnaud Maret. 2026-05-04. Invariant measures for Deroin-Tholozan representations. https://arxiv.org/abs/2605.02823

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