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Bers isomorphism on the universal Teichm\"uller curve

Authors
  • Teo, Lee-Peng
Type
Published Article
Publication Date
Jul 14, 2006
Submission Date
Jul 14, 2006
Identifiers
arXiv ID: math/0607336
Source
arXiv
License
Unknown
External links

Abstract

We study the Bers isomorphism between the Teichm\"uller space of the parabolic cyclic group and the universal Teichm\"uller 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 Teichm\"uller 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 Teichm\"uller curve via the Bers isomorphism.

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