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

Abstract : 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 Fuch-sian 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.
Liste complète des métadonnées

Littérature citée [16 références]  Voir  Masquer  Télécharger

https://hal-ens.archives-ouvertes.fr/hal-01792650
Contributeur : Marine Laffont <>
Soumis le : mardi 15 mai 2018 - 16:08:16
Dernière modification le : mercredi 10 octobre 2018 - 10:09:13
Document(s) archivé(s) le : mardi 25 septembre 2018 - 10:00:52

Fichier

SO2NHiggsBundles.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01792650, version 1

Citation

Brian Collier, Nicolas Tholozan, Jérémy Toulisse. The geometry of maximal representations of surface groups into SO0 (2, n). 2017. 〈hal-01792650〉

Partager

Métriques

Consultations de la notice

41

Téléchargements de fichiers

15