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Coordinates for the moduli space of flat PSL(2,R)-connections

R. M. Kashaev
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Abstract

Let M be the moduli space of irreducible flat PSL(2,R) connections on a punctured surface of finite type with parabolic holonomies around punctures. By using a notion of admissibility of an ideal arc, M is covered by dense open subsets associated to ideal triangulations of the surface. A principal bundle over M is constructed which, when restricted to the Teichmuller component of M, is isomorphic to the decorated Teichmuller space of Penner. The construction gives a generalization to M of Penner's coordinates for the Teichmuller space.

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R. M. Kashaev. 2003-07-13. Coordinates for the moduli space of flat PSL(2,R)-connections. https://arxiv.org/abs/math/0307186

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