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

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

2003-07-13

arxiv.org/abs/math/0307186v1

Mathematics

Geometric Topology

12 pages, no figures

Scientific paper

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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