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Moduli spaces of local systems and higher Teichmüller theory

Vladimir Fock, Alexander Goncharov (2006)

Publications Mathématiques de l'IHÉS

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 closely...

Moduli spaces of stable pairs and non-abelian zeta functions of curves via wall-crossing

Sergey Mozgovoy, Markus Reineke (2014)

Journal de l’École polytechnique — Mathématiques

In this paper we study and relate the non-abelian zeta functions introduced by Weng and invariants of the moduli spaces of arbitrary rank stable pairs over curves. We prove a wall-crossing formula for the latter invariants and obtain an explicit formula for these invariants in terms of the motive of a curve. Previously, formulas for these invariants were known only for rank 2 due to Thaddeus and for rank 3 due to Muñoz. Using these results we obtain an explicit formula for the non-abelian zeta functions,...

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