Configurations of flags and representations of surface groups in complex hyperbolic geometry

Julien Marché (1) , Pierre Will (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 IF - Institut Fourier

In this work, we describe a set of coordinates on the PU(2,1)-representation variety of the fundamental group of an oriented punctured surface Σ with negative Euler characteristic. The main technical tool we use is a set of geometric invariants of a triple of flags in the complex hyperbolic plane H2C . We establish a bijection between a set of decorations of an ideal triangulation of Σ and a subset of the PU(2,1)-representation variety of π 1(Σ).

Domaines: Mathématiques [math]

Julien Marché, Pierre Will. Configurations of flags and representations of surface groups in complex hyperbolic geometry. Geom. Dedicata, 2012, 156, pp.49-70. ⟨hal-00843249⟩