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

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 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).
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https://hal.archives-ouvertes.fr/hal-00843249
Contributor : Carole Juppin Connect in order to contact the contributor
Submitted on : Wednesday, July 10, 2013 - 10:12:46 PM
Last modification on : Tuesday, May 11, 2021 - 11:36:03 AM

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  • HAL Id : hal-00843249, version 1

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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⟩

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