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.
Poisson structures on the Teichmuller space of hyperbolic surfaces with conical points / Mondello, Gabriele. - STAMPA. - 510(2010), pp. 307-329. ((Intervento presentato al convegno 4th Ahlfors-Bers Colloquium tenutosi a Newark, NJ nel MAY 08-11, 2008. - CONTEMPORARY MATHEMATICS. [10.1090/conm/510/10030].
Poisson structures on the Teichmuller space of hyperbolic surfaces with conical points
MONDELLO, GABRIELE
2010
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
