Mathematics – Differential Geometry
Scientific paper
2008-12-09
Mathematics
Differential Geometry
23 pages, 2 figures. Two mistakes in the description of the holonomy map are corrected. Exposition improved and more details a
Scientific paper
In this paper two Poisson structures on the moduli space of hyperbolic
surfaces with conical points are compared: the Weil-Petersson one and the \eta
coming from the representation variety. We show that they are multiple of each
other, if the angles do not exceed 2\pi. Moreover, we exhibit an explicit
formula for \eta in terms of hyperbolic lengths of a suitable system of arcs.
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