1 November 2009 A symplectic map between hyperbolic and complex Teichmüller theory
Kirill Krasnov, Jean-Marc Schlenker
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Duke Math. J. 150(2): 331-356 (1 November 2009). DOI: 10.1215/00127094-2009-054


Let S be a closed, orientable surface of genus at least 2. The space TH×ML, where TH is the “hyperbolic” Teichmüller space of S and ML is the space of measured geodesic laminations on S, is naturally a real symplectic manifold. The space CP of complex projective structures on S is a complex symplectic manifold. A relation between these spaces is provided by Thurston's grafting map Gr. We prove that this map, although not smooth, is symplectic. The proof uses a variant of the renormalized volume defined for hyperbolic ends


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Kirill Krasnov. Jean-Marc Schlenker. "A symplectic map between hyperbolic and complex Teichmüller theory." Duke Math. J. 150 (2) 331 - 356, 1 November 2009. https://doi.org/10.1215/00127094-2009-054


Published: 1 November 2009
First available in Project Euclid: 16 October 2009

zbMATH: 1206.30058
MathSciNet: MR2569616
Digital Object Identifier: 10.1215/00127094-2009-054

Primary: 30F60
Secondary: 32G15

Rights: Copyright © 2009 Duke University Press

Vol.150 • No. 2 • 1 November 2009
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