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math.GT2026
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…
math.GT2025
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…
math.GT2024
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…