Dominating Surface Group Representations by Fuchsian Ones

By B. Deroin, Nicolas Tholozan. 2013

49 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/58f564227f6913ef6b2323328b091b77bccc6557

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Nicolas Tholozan
2. J'er'emy Toulisse
3. Brian Collier
4. Anna Wienhard

In Mathematical Physics

1. Nicolas Tholozan
2. J'er'emy Toulisse
3. Brian Collier
4. Anna Wienhard

Citations in the corpus

• The geometry of maximal representations of surface groups into SO0(2,n) (2017, result): “This should be compared to [DT16] where Deroin and the second author prove that for any representation ρ into the isometry group of H, there exists a Fuchsian representation j such that Lj ≥ Lρ.”