Geometry & Topology

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

Brice Loustau

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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. Generalizations of results of C McMullen are derived, notably quasifuchsian reciprocity. The symplectic geometry is also described in a Hamiltonian setting with the complex Fenchel–Nielsen coordinates on quasifuchsian space, recovering results of I Platis.

Article information

Geom. Topol., Volume 19, Number 3 (2015), 1737-1775.

Received: 25 June 2014
Accepted: 9 January 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D30: Symplectic structures of moduli spaces

complex projective structures symplectic structures Teichmüller theory character variety quasifuchsian structures


Loustau, Brice. The complex symplectic geometry of the deformation space of complex projective structures. Geom. Topol. 19 (2015), no. 3, 1737--1775. doi:10.2140/gt.2015.19.1737.

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