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Mathematics > Differential Geometry

arXiv:0710.3327 (math)
[Submitted on 17 Oct 2007]

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

Authors:Julien Marche, Pierre Will
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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 $\pi_1(S)$.
Comments: 23 pages, 2 figures
Subjects: Differential Geometry (math.DG)
MSC classes: 57S30; 51M10; 57M50
Cite as: arXiv:0710.3327 [math.DG]
  (or arXiv:0710.3327v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.3327

Submission history

From: Marche Julien [view email]
[v1] Wed, 17 Oct 2007 15:38:58 UTC (28 KB)
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