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Kähler groups, real hyperbolic spaces and the Cremona group. With an appendix by Serge Cantat

  • Thomas Delzant (a1) and Pierre Py (a2)


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 three factors through a homomorphism onto a cocompact discrete subgroup of PSL2(ℝ). We also study actions of Kähler groups on infinite-dimensional real hyperbolic spaces, describe some exotic actions of PSL2(ℝ) on these spaces, and give an application to the study of the Cremona group.

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