Mathematics – Differential Geometry
Scientific paper
2007-10-17
Mathematics
Differential Geometry
23 pages, 2 figures
Scientific paper
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 $\pi_1(S)$.
Marche Julien
Will Pierre
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