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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Volume 253, Pages 175–203
(Mi tm92)
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Kähler Geometry of the Universal Teichmüller Space and Coadjoint Orbits of the Virasoro Group
A. G. Sergeev Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
The Kähler geometry of the universal Teichmüller space and related infinite-dimensional Kähler manifolds is studied. The universal Teichmüller space $\mathcal T$ may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The classical Teichmüller spaces $T(G)$, where $G$ is a Fuchsian group, are contained in $\mathcal T$ as complex Kähler submanifolds. The homogeneous spaces $\text {Diff}_+(S^1)/\text {M\"ob}(S^1)$ and $\text {Diff}_+(S^1)/S^1$ of the diffeomorphism group $\text {Diff}_+(S^1)$ of the unit circle are closely related to $\mathcal T$. They are Kähler Frechet manifolds that can be realized as coadjoint orbits of the Virasoro group (and exhaust all coadjoint orbits of this group that have the Kähler structure).
Received in October 2005
Citation:
A. G. Sergeev, “Kähler Geometry of the Universal Teichmüller Space and Coadjoint Orbits of the Virasoro Group”, Complex analysis and applications, Collected papers, Trudy Mat. Inst. Steklova, 253, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 175–203; Proc. Steklov Inst. Math., 253 (2006), 160–185
Linking options:
https://www.mathnet.ru/eng/tm92 https://www.mathnet.ru/eng/tm/v253/p175
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Abstract page: | 459 | Full-text PDF : | 133 | References: | 63 |
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