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Geometriae Dedicata

, Volume 156, Issue 1, pp 49–70 | Cite as

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

  • Julien Marché
  • Pierre Will
Original Paper
  • 91 Downloads

Abstract

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 \({\bf H^2_{\mathbb {C}}}\) . 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).

Keywords

Complex hyperbolic geometry Representations of surface group Decorated triangulation 

Mathematics Subject Classification (2000)

22E40 32M15 51M10 57M50 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Centre de Mathématiques, Laurent Schwarz, Ecole PolytechniquePalaiseauFrance
  2. 2.Institut Fourier, Université Joseph FourierSt-Martin d’HèresFrance

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