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Dominating surface group representations by Fuchsian ones

Abstract : We prove that a representation from the fundamental group of a closed surface of negative Euler characteristic with values in the isometry group of a Riemannian manifold of sectional curvature bounded by -1 can be dominated by a Fuchsian representation. Moreover, we prove that the domination can be made strict, unless the representation is discrete and faithful in restriction to an invariant totally geodesic 2-plane of curvature -1. When applied to representations into PSL(2,R) of non-extremal Euler class, our result is a step forward in understanding the space of closed anti-de Sitter 3-manifolds. For representations into PSU(n,1), it sheds a new light on a famous theorem by Toledo.
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https://hal.archives-ouvertes.fr/hal-00936075
Contributor : Nicolas Tholozan Connect in order to contact the contributor
Submitted on : Friday, January 24, 2014 - 2:31:18 PM
Last modification on : Sunday, June 26, 2022 - 12:00:43 PM

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  • HAL Id : hal-00936075, version 1
  • ARXIV : 1311.2919

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Bertrand Deroin, Nicolas Tholozan. Dominating surface group representations by Fuchsian ones. 2013. ⟨hal-00936075⟩

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