Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces

François Fillastre (1) , Andrea Seppi (2)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 IF - Institut Fourier

A well-known theorem of Wolpert shows that the Weil–Petersson symplectic form on Teichmüller space, computed on two infinitesimal twists along simple closed geodesics on a fixed hyperbolic surface, equals the sum of the cosines of the intersection angles. We define an infinitesimal deformation starting from a more general object, namely a balanced geodesic graph, by which any tangent vector to Teichmüller space can be represented. We then prove a generalization of Wolpert's formula for these deformations. In the case of simple closed curves, we recover the theorem of Wolpert.

Domaines: Topologie géométrique [math.GT]

François Fillastre, Andrea Seppi. Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces. Annales Henri Lebesgue, 2020, 3, pp.873-899. ⟨10.5802/ahl.48⟩. ⟨hal-01675473v1⟩