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

Abstract

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.

21 pages, 11 figures

References in corpus (2)

• Area-preserving diffeomorphism of the hyperbolic plane and K-surfaces in Anti-de Sitter space
• The complex symplectic geometry of the deformation space of complex projective structures

Cited by in corpus (1)

• Affine deformations of quasi-divisible convex cones