9 papers
Invariant measures for Deroin-Tholozan representations
Yohann Bouilly, Arnaud Maret
We classify mapping class group invariant probability measures on the character varieties of Deroin-Tholozan representations, namely the compact components of relative $\mathrm{PSL…
On the symplectic geometry of branched hyperbolic surfaces in genus two
Gianluca Faraco, Arnaud Maret
We construct analogues of Fenchel-Nielsen coordinates on an open and dense subset of the space of holonomies of branched hyperbolic structures on a closed genus-2 surface. We show…
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…
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…
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…
The geometry of Deroin-Tholozan representations
Aaron Fenyes, Arnaud Maret
We present a way to build hyperbolic spheres with conical singularities by gluing together simple building blocks. Our construction provides good control over the holonomy of the r…
Proceedings of the Young Researchers Workshop on Positivity in Lie Groups
Xenia Flamm, Arnaud Maret
These notes transcribe a workshop about the notion of total positivity and -positivity and its relation to Higher Teichmüller Theory. -positivity is a notion of positivity in…
Action-angle coordinates for surface group representations in genus zero
Arnaud Maret
We study a compact family of totally elliptic representations of the fundamental group of a punctured sphere into discovered by Deroin and Tholozan and…
Ergodicity of the mapping class group action on Deroin-Tholozan representations
Arnaud Maret
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…