For d=3 the limit cones of multi-Fuchsian representations can have finitely many sides scaling with genus, dense boundary rays, or vary discontinuously with the representation.
Convex structures of the unit tangent spheres in Teichmüller space.ArXiv 2503.20404 (2025)
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Proves dimension formulas for faces of unit spheres in Teichmüller space with Thurston metric, basepoint independence of combinatorial structure, and natural isomorphisms between extended mapping class groups and combinatorial automorphism groups of the spheres for genus ≥2.
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Limit cones of multi-Fuchsian representations
For d=3 the limit cones of multi-Fuchsian representations can have finitely many sides scaling with genus, dense boundary rays, or vary discontinuously with the representation.
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The combinatorial structure of the unit tangent spheres and cotangent spheres of Teichm{\"u}ller space with Thurston's Finsler metric
Proves dimension formulas for faces of unit spheres in Teichmüller space with Thurston metric, basepoint independence of combinatorial structure, and natural isomorphisms between extended mapping class groups and combinatorial automorphism groups of the spheres for genus ≥2.