English

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

Differential Geometry 2007-10-18 v1

Abstract

We describe a set of coordinates on the PU(2,1)-representation variety of the fundamental group of an oriented punctured surface SS 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 SS and a subset of the PU(2,1)-representation variety of π1(S)\pi_1(S).

Cite

@article{arxiv.0710.3327,
  title  = {A la Fock-Goncharov coordinates for PU(2,1)},
  author = {Julien Marche and Pierre Will},
  journal= {arXiv preprint arXiv:0710.3327},
  year   = {2007}
}

Comments

23 pages, 2 figures

R2 v1 2026-06-21T09:33:10.684Z