Ergodic mapping class group invariant measures on Deroin-Tholozan character varieties are either counting measures on finite orbits or the Liouville measure from the Goldman symplectic form.
Groups Geom
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A survey organizing known results on the dynamics of mapping class group actions on character varieties of surface groups, emphasizing the compact-versus-non-compact dichotomy and covering PSL(2,R), compact groups, PSL(2,C), and higher-rank Lie groups.
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Invariant measures for Deroin-Tholozan representations
Ergodic mapping class group invariant measures on Deroin-Tholozan character varieties are either counting measures on finite orbits or the Liouville measure from the Goldman symplectic form.