Bulletin of the American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

A period mapping in universal Teichmüller space

Author(s): Subhashis Nag
Journal: Bull. Amer. Math. Soc. 26 (1992), 280-287.
MSC (2000): Primary 32G20; Secondary 30F60, 32G15, 81S10, 81T30
MathSciNet review: 1121571
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Abstract: In previous work it had been shown that the remarkable homogeneous space $M = \operatorname{Diff}({S^1})/{\text{PSL}}(2,\mathbb{R})$ sits as a complex analytic and Kähler submanifold of the Universal Teichmüller Space. There is a natural immersion $\prod$ of M into the infinite-dimensional version (due to Segal) of the Siegel space of period matrices. That map $\prod$ is proved to be injective, equivariant, holomorphic, and Kähler-isometric (with respect to the canonical metrics). Regarding a period mapping as a map describing the variation of complex structure, we explain why $\prod$ is an infinite-dimensional period mapping.

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