Kodai Mathematical Journal

The effect of Fenchel-Nielsen coordinates under elementary moves

Dong Tan, Peijia Liu, and Xuewen Liu

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We describe the effect of Fenchel-Nielsen coordinates under elementary move for hyperbolic surfaces with geodesic boundaries, punctures and cone points, which generalize Okai's result for surfaces with geodesic boundaries. The proof relies on the parametrization of the Teichmüller space of surface of type (1,1) or (0,4) as a sub-locus of an algebraic equation in $\mathbf{R}^3$. As an application, we show that the hyperbolic length functions of closed curves are asymptotically piecewise linear functions with respect to the Fenchel Nielsen coordinates in the Teichmüller spaces of surfaces with cone points.

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Kodai Math. J., Volume 41, Number 2 (2018), 421-439.

First available in Project Euclid: 2 July 2018

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Tan, Dong; Liu, Peijia; Liu, Xuewen. The effect of Fenchel-Nielsen coordinates under elementary moves. Kodai Math. J. 41 (2018), no. 2, 421--439. doi:10.2996/kmj/1530496851. https://projecteuclid.org/euclid.kmj/1530496851

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