A la Fock-Goncharov coordinates for PU(2,1)

2007/10/17 by Julien Marché, Marche, Julien, Pierre Will +1
Mathematics · #51M10 #57M50 #57S30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0710.3327

openalex publication_date 2007/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a set of coordinates on the PU(2,1)-representation variety of the fundamental group of an oriented punctured surface S with negative Euler characteristic. The main technical tool we use is a set of geometric invariants of a triple of flags in the complex hyperpolic plane. We establish a bijection between a set of decorations of an ideal triangulation of S and a subset of the PU(2,1)-representation variety of π₁(S).

Citations

• Dual Teichmuller and lamination spaces

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