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Bers isomorphism on the universal Teichmüller curve

Lee-Peng Teo
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Abstract

We study the Bers isomorphism between the Teichmüller space of the parabolic cyclic group and the universal Teichmüller curve. We prove that this is a group isomorphism and its derivative map gives a remarkable relation between Fourier coefficients of cusp forms and Fourier coefficients of vector fields on the unit circle. We generalize the Takhtajan-Zograf metric to the Teichmüller space of the parabolic cyclic group, and prove that up to a constant, it coincides with the pull back of the Velling-Kirillov metric defined on the universal Teichmüller curve via the Bers isomorphism.

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Lee-Peng Teo. 2006-07-14. Bers isomorphism on the universal Teichmüller curve. https://arxiv.org/abs/math/0607336

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