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math.RT2024
Totally elliptic surface group representations
Arnaud Maret
A surface group representation into a Lie group is called totally elliptic if every simple closed curve on the surface is mapped to an elliptic element of the target group. In this…
math.DS2024
Mapping class group orbit closures for Deroin-Tholozan representations
Yohann Bouilly, Gianluca Faraco, Arnaud Maret
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 orb…
math.DS2024
Tykhyy's Conjecture on finite mapping class group orbits
Samuel Bronstein, Arnaud Maret
We classify the finite orbits of the mapping class group action on the character variety of Deroin--Tholozan representations of punctured spheres. In particular, we prove that the…