arXiv 1711.034292017-11math.GT

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

François Fillastre, Andrea Seppi

备注：: 21 pages, 11 figures
发表信息：: Annales Henri Lebesgue, 3 (2020), 873-899
DOI：: 10.5802/ahl.48

英文摘要：

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.

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