Duke Mathematical Journal
- Duke Math. J.
- Volume 150, Number 2 (2009), 331-356.
A symplectic map between hyperbolic and complex Teichmüller theory
Let be a closed, orientable surface of genus at least . The space , where is the “hyperbolic” Teichmüller space of and is the space of measured geodesic laminations on , is naturally a real symplectic manifold. The space of complex projective structures on is a complex symplectic manifold. A relation between these spaces is provided by Thurston's grafting map . We prove that this map, although not smooth, is symplectic. The proof uses a variant of the renormalized volume defined for hyperbolic ends
Duke Math. J., Volume 150, Number 2 (2009), 331-356.
First available in Project Euclid: 16 October 2009
Permanent link to this document
Digital Object Identifier
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