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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| Format: | Article |
| Language: | English |
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SPRINGER
2007
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| Online Access: | http://shdl.mmu.edu.my/3043/ http://shdl.mmu.edu.my/3043/1/1066.pdf |
| _version_ | 1848790218127179776 |
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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. |
| first_indexed | 2025-11-14T18:09:07Z |
| format | Article |
| id | mmu-3043 |
| institution | Multimedia University |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:09:07Z |
| publishDate | 2007 |
| publisher | SPRINGER |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |