The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space
In the first part of the paper we describe the complex geometry of the universal Teichmüller space T, which may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The quotient S of the diffeomorphism group of the circle modulo Möbius tr...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149245 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space / A.G. Sergeev // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862721024666107904 |
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| author | Sergeev, A.G. |
| author_facet | Sergeev, A.G. |
| citation_txt | The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space / A.G. Sergeev // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In the first part of the paper we describe the complex geometry of the universal Teichmüller space T, which may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The quotient S of the diffeomorphism group of the circle modulo Möbius transformations may be treated as a smooth part of T. In the second part we consider the quantization of universal Teichmüller space T. We explain first how to quantize the smooth part S by embedding it into a Hilbert-Schmidt Siegel disc. This quantization method, however, does not apply to the whole universal Teichmüller space T, for its quantization we use an approach, due to Connes.
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| first_indexed | 2025-12-07T18:28:34Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149245 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:28:34Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sergeev, A.G. 2019-02-19T19:17:48Z 2019-02-19T19:17:48Z 2009 The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space / A.G. Sergeev // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 18 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 58E20; 53C28; 32L25 https://nasplib.isofts.kiev.ua/handle/123456789/149245 In the first part of the paper we describe the complex geometry of the universal Teichmüller space T, which may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The quotient S of the diffeomorphism group of the circle modulo Möbius transformations may be treated as a smooth part of T. In the second part we consider the quantization of universal Teichmüller space T. We explain first how to quantize the smooth part S by embedding it into a Hilbert-Schmidt Siegel disc. This quantization method, however, does not apply to the whole universal Teichmüller space T, for its quantization we use an approach, due to Connes. This paper is a contribution to the Special Issue on Kac–Moody Algebras and Applications. While preparing this paper, the author was partly supported by the RFBR grants 06-02-04012, 08-01-00014, by the program of Support of Scientific Schools (grant NSH-3224.2008.1), and by the Scientific Program of RAS “Nonlinear Dynamics”. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space Article published earlier |
| spellingShingle | The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space Sergeev, A.G. |
| title | The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space |
| title_full | The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space |
| title_fullStr | The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space |
| title_full_unstemmed | The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space |
| title_short | The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space |
| title_sort | group of quasisymmetric homeomorphisms of the circle and quantization of the universal teichmüller space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149245 |
| work_keys_str_mv | AT sergeevag thegroupofquasisymmetrichomeomorphismsofthecircleandquantizationoftheuniversalteichmullerspace AT sergeevag groupofquasisymmetrichomeomorphismsofthecircleandquantizationoftheuniversalteichmullerspace |