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1 results

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

  • Part of
  • Thomas Delzant, Pierre Py
  • Journal:
    Compositio Mathematica / Volume 148 / Issue 1 / January 2012
    Published online by Cambridge University Press:
    30 November 2011, pp. 153-184
    Print publication:
    January 2012
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  • 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.