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The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space
Інший ID:
2000 Mathematics Subject Classification: 58E20; 53C28; 32L25
Посилання:
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.
Підтримка:
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”.
Дата:
2009
Переглядів:
307
Завантажень:
193
Анотація:
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.
