## Geometry & Topology

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

Brice Loustau

#### 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. 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

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

Dates
Accepted: 9 January 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510858774

Digital Object Identifier
doi:10.2140/gt.2015.19.1737

Mathematical Reviews number (MathSciNet)
MR3352248

Zentralblatt MATH identifier
1318.53097

Subjects
Primary: 53D30: Symplectic structures of moduli spaces

#### Citation

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. https://projecteuclid.org/euclid.gt/1510858774

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