Compact anti-de Sitter 3-manifolds and folded hyperbolic structures on surfaces

François Guéritaud; Fanny Kassel; Maxime Wolff

doi:10.2140/pjm.2015.275.325

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arXiv · 1311.2804

Compact anti-de Sitter 3-manifolds and folded hyperbolic structures on surfaces

François Guéritaud·Fanny Kassel·Maxime Wolff

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Abstract

We prove that any nonabelian, non-Fuchsian representation of a surface group into PSL(2,R) is the holonomy of a folded hyperbolic structure on the surface. Using similar ideas, we establish that any non-Fuchsian representation rho of a surface group into PSL(2,R) is strictly dominated by some Fuchsian representation j, in the sense that the hyperbolic translation lengths for j are uniformly larger than for rho; conversely, any Fuchsian representation j strictly dominates some non-Fuchsian representation rho, whose Euler class can be prescribed. This has applications to compact anti-de Sitter 3-manifolds.

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François Guéritaud, Fanny Kassel, Maxime Wolff. 2013-11-12. Compact anti-de Sitter 3-manifolds and folded hyperbolic structures on surfaces. https://doi.org/10.2140/pjm.2015.275.325

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