Length series on Teichmuller space
نویسنده
چکیده
We prove that a certain series defines a constant function using Wolpert’s formula for the variation of the length of a geodesic along a Fenchel Nielsen twist. Subsequently we determine the value viewing it as function on the the Deligne Mumford compactification M1,1 and evaluating it at the stable curve at infinity. Conventions: 1. For γ an essential closed curve on a surface lγ(x) is the length of the geodesic homotopic to γ where x is the point in the moduli space determined by the metric on the surface. 2. For a homeomorphism h : M → M and a geodesic γ, h(γ) is the geodesic homotopic to the image of γ under h. 3. if γ is an oriented curve then −γ is the curve with the opposite orientation.
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