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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Volume 253, Pages 175–203 (Mi tm92)  

Kähler Geometry of the Universal Teichmüller Space and Coadjoint Orbits of the Virasoro Group

A. G. Sergeev

Steklov Mathematical Institute, Russian Academy of Sciences
References:
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
English version:
Proceedings of the Steklov Institute of Mathematics, 2006, Volume 253, Pages 160–185
DOI: https://doi.org/10.1134/S0081543806020143
Bibliographic databases:
Document Type: Article
UDC: 515.17
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Ser06}
\by A.~G.~Sergeev
\paper K\"ahler Geometry of the Universal Teichm\"uller Space and Coadjoint Orbits of the Virasoro Group
\inbook Complex analysis and applications
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2006
\vol 253
\pages 175--203
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm92}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2338696}
\zmath{https://zbmath.org/?q=an:1351.32023}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 253
\pages 160--185
\crossref{https://doi.org/10.1134/S0081543806020143}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748310532}
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