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arXiv · 1708.09052

On Kawai theorem for orbifold Riemann surfaces

Leon A Takhtajan
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Abstract

We prove a generalization of Kawai theorem for the case of orbifold Riemann surface. The computation is based on a formula for the differential of a holomorphic map from the cotangent bundle of the Teichmüller space to the $\mathrm{PSL}(2,\mathbb{C})$-character variety, which allows to evaluate explicitly the pullback of Goldman symplectic form in the spirit of Riemann bilinear relations. As a corollary, we obtain a generalization of Goldman's theorem that the pullback of Goldman symplectic from on $\mathrm{PSL}(2,\mathbb{R})$-character variety is a symplectic form of the Weil-Petersson metric on the Teichmüller space.

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Leon A Takhtajan. 2018-08-08. On Kawai theorem for orbifold Riemann surfaces. https://arxiv.org/abs/1708.09052

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