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A period mapping in universal Teichmüller space

Author: 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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