Geometriae Dedicata

, Volume 137, Issue 1, pp 27–61 | Cite as

Sous-groupes discrets de PU(2,1) engendrés par n réflexions complexes et Déformation

Original Paper


Let PU(2,1) be the group of holomorphic isometries in the hyperbolic complex plane \({{\mathbb{H}}^2_{\mathbb{C}}}\) and let G n be a sub-group of PU(2,1) which is generated by n complex reflections with respect to complex lines in \({{{\mathbb{H}}^2_{\mathbb{C}}}}\) . Under certain conditions, we prove that G n is discrete. We construct representations ρ of the fundamental group Γ g of the compact surface Σ g of genus g, into PU(2,1), we prove they are discrete, faithful and we compute the dimension their deformation space.


Complex reflection Discrete sub-group Surface fundamental group Representation of the fundamental group of the compact surface Toledo’s invariant Representation manifold Deformation 

Mathematics Subject Classification (2000)

32Q05 20H10 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Èquipe Analyse AlgébriqueInstitut de Mathématiques de JussieuParisFrance

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