The geometry of maximal representations of surface groups into SO0(2,n)

By Brian Collier, Nicolas Tholozan, J'er'emy Toulisse. Duke mathematical journal, 2017

81 citations recorded by the source corpus.

In this paper, we study the geometric and dynamical properties of maximal representations of surface groups into Hermitian Lie groups of rank 2. Combining tools from Higgs bundle theory, the theory of Anosov representations, and pseudo-Riemannian geometry, we obtain various results of interest. We prove that these representations are holonomies of certain geometric structures, recovering results of Guichard and Wienhard. We also prove that their length spectrum is uniformly bigger than that of a suitably chosen Fuchsian representation, extending a previous work of the second author. Finally, we show that these representations preserve a unique minimal surface in the symmetric space, extending a theorem of Labourie for Hitchin representations in rank 2.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6b51dbe99439e629b2059d8faadb99e63ae35a38

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. Anna Wienhard
2. Andr'es Sambarino
3. Minju M. Lee
4. H. Oh
5. Michael Kapovich
6. B. Leeb

In Mathematical Physics

1. Anna Wienhard
2. Andr'es Sambarino
3. Minju M. Lee
4. H. Oh
5. Michael Kapovich
6. B. Leeb
7. Olivier Y Guichard

Citations in the corpus

• An invitation to higher Teichm\"uller theory (2018, background): “For maximal representations we expect similarly to get a mapping class group invariant projection from T max(S,G) to T (S), see [2, Conjecture 10]. For G = SO(2,n) such a projection is constructed in [33]. For G of rank 2 Alessandini and Collier [2] construct a mapping class group invariant complex ”