Rigidity and flexibility of triangle groups in complex hyperbolic geometry

Elisha Falbel (1, 2) , Pierre-Vincent Koseleff (1, 2)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We show that the Teichmüller space of the triangle groups of type (p,q,∞) in the automorphism group of the two-dimensional complex hyperbolic space contains open sets of 0, 1 and two real dimensions. In particular, we identify the Teichmüller space near embeddings of the modular group preserving a complex geodesic.

Mots clés: Complex hyperbolic; Triangle group; Discrete group; Rigidity; CR-manifolds

Domaines: Mathématiques [math]

Elisha Falbel, Pierre-Vincent Koseleff. Rigidity and flexibility of triangle groups in complex hyperbolic geometry. Topology, 2002, 41 (4), pp.767-786. ⟨10.1016/S0040-9383(00)00049-5⟩. ⟨hal-01362297⟩