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The complex symplectic geometry of the deformation space of complex projective structures

Abstract : This article investigates the complex symplectic geometry of the deformation space of complex projective structures on a closed oriented surface of genus at least 2. The cotangent symplectic structure given by the Schwarzian parametrization is studied carefully and compared to the Goldman symplectic structure on the character variety, clarifying and generalizing a theorem of S. Kawai [Kaw96]. Generalizations of results of C. McMullen are derived, notably quasi-Fuchsian reciprocity [McM00]. The symplectic geometry is also described in a Hamiltonian setting with the complex Fenchel-Nielsen coordinates on quasi-Fuchsian space, recovering results of I. Platis [Pla01].
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https://hal.archives-ouvertes.fr/hal-01275182
Contributor : Brice Loustau <>
Submitted on : Wednesday, February 17, 2016 - 3:56:44 AM
Last modification on : Wednesday, September 16, 2020 - 4:05:32 PM
Long-term archiving on: : Wednesday, May 18, 2016 - 1:12:38 PM

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Brice Loustau. The complex symplectic geometry of the deformation space of complex projective structures. 2016. ⟨hal-01275182⟩

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