# Moduli spaces of local systems and higher Teichmüller theory

@article{Fock2003ModuliSO, title={Moduli spaces of local systems and higher Teichm{\"u}ller theory}, author={Vladimir V. Fock and Alexander B. Goncharov}, journal={Publications Math{\'e}matiques de l'Institut des Hautes {\'E}tudes Scientifiques}, year={2003}, volume={103}, pages={1-211} }

Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces…

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