Kähler groups, real hyperbolic spaces and the Cremona group

Abstract

Generalizing a classical theorem of Carlson and Toledo, we prove that any Zariski dense isometric action of a Kähler group on the real hyperbolic space of dimension at least 3 factors through a homomorphism onto a cocompact discrete subgroup of PSL(2,R). We also study actions of Kähler groups on infinite dimensional real hyperbolic spaces, describe some exotic actions of PSL(2,R) on these spaces, and give an application to the study of the Cremona group.

Referee's comments and minor corrections included. With an appendix by Serge Cantat

References in corpus (2)

• On the classification of rank two representations of quasiprojective fundamental groups
• Sous-groupes algébriques du groupe de Cremona

Cited by in corpus (7)

• Infinite dimensional non-positively curved symmetric spaces of finite rank
• Coxeter groups and Kähler groups
• Random walks, WPD actions, and the Cremona group
• Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces
• Hyperbolic spaces, principal series and $\mathrm{O}(2,\infty )$
• Representations of infinite dimension orthogonal groups of quadratic forms with finite index
• Les groupes de Burger-Mozes ne sont pas kählériens