Duke Mathematical Journal

A symplectic map between hyperbolic and complex Teichmüller theory

Kirill Krasnov and Jean-Marc Schlenker

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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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Duke Math. J., Volume 150, Number 2 (2009), 331-356.

First available in Project Euclid: 16 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30F60: Teichmüller theory [See also 32G15]
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]


Krasnov, Kirill; Schlenker, Jean-Marc. A symplectic map between hyperbolic and complex Teichmüller theory. Duke Math. J. 150 (2009), no. 2, 331--356. doi:10.1215/00127094-2009-054. https://projecteuclid.org/euclid.dmj/1255699343

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