Poisson structures on the Teichmueller space of hyperbolic surfaces with conical points

Details Poisson structures on the Teichmueller space of hyperbolic surfaces with conical points Poisson structures on the Teichmueller space of hyperbolic surfaces with conical points

2008-12-09

arxiv.org/abs/0812.1602v2

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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