Bers isomorphism on the universal Teichmüller curve

We study the Bers isomorphism between the Teichmuller space of the parabolic cyclic group and the universal Teichmuller 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 fi...

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Main Author: Teo, Lee-Peng
Format: Article
Language:English
Published: SPRINGER 2007
Subjects:
Online Access:http://shdl.mmu.edu.my/3043/
http://shdl.mmu.edu.my/3043/1/1066.pdf
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author Teo, Lee-Peng
author_facet Teo, Lee-Peng
author_sort Teo, Lee-Peng
building MMU Institutional Repository
collection Online Access
description We study the Bers isomorphism between the Teichmuller space of the parabolic cyclic group and the universal Teichmuller 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 Teichmuller 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 Teichmuller curve via the Bers isomorphism.
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spelling mmu-30432014-02-27T07:29:19Z http://shdl.mmu.edu.my/3043/ Bers isomorphism on the universal Teichmüller curve Teo, Lee-Peng T Technology (General) QA75.5-76.95 Electronic computers. Computer science We study the Bers isomorphism between the Teichmuller space of the parabolic cyclic group and the universal Teichmuller 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 Teichmuller 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 Teichmuller curve via the Bers isomorphism. SPRINGER 2007-07 Article NonPeerReviewed text en http://shdl.mmu.edu.my/3043/1/1066.pdf Teo, Lee-Peng (2007) Bers isomorphism on the universal Teichmüller curve. Mathematische Zeitschrift, 256 (3). 603-613 . ISSN 0025-5874 http://dx.doi.org/10.1007/s00209-006-0089-9 doi:10.1007/s00209-006-0089-9 doi:10.1007/s00209-006-0089-9
spellingShingle T Technology (General)
QA75.5-76.95 Electronic computers. Computer science
Teo, Lee-Peng
Bers isomorphism on the universal Teichmüller curve
title Bers isomorphism on the universal Teichmüller curve
title_full Bers isomorphism on the universal Teichmüller curve
title_fullStr Bers isomorphism on the universal Teichmüller curve
title_full_unstemmed Bers isomorphism on the universal Teichmüller curve
title_short Bers isomorphism on the universal Teichmüller curve
title_sort bers isomorphism on the universal teichmüller curve
topic T Technology (General)
QA75.5-76.95 Electronic computers. Computer science
url http://shdl.mmu.edu.my/3043/
http://shdl.mmu.edu.my/3043/
http://shdl.mmu.edu.my/3043/
http://shdl.mmu.edu.my/3043/1/1066.pdf