Moduli spaces of local systems and higher Teichmüller theory
Let G be a split semisimple algebraic group over with trivial center. Let S be a compact oriented surface, with or without boundary. We define representations of the fundamental group of S to G(), 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 closely related...