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Tr. Mat. Inst. 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

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 $\text {Diff}_+(S^1)/\text {Möb}(S^1)$ 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).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 253, 160–185

Bibliographic databases:

UDC: 515.17
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, Tr. 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 Tr. 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://www.ams.org/mathscinet-getitem?mr=2338696}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 253
\pages 160--185
\crossref{https://doi.org/10.1134/S0081543806020143}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748310532}


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