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2015 The complex symplectic geometry of the deformation space of complex projective structures
Brice Loustau
Geom. Topol. 19(3): 1737-1775 (2015). DOI: 10.2140/gt.2015.19.1737

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.

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Brice Loustau. "The complex symplectic geometry of the deformation space of complex projective structures." Geom. Topol. 19 (3) 1737 - 1775, 2015. https://doi.org/10.2140/gt.2015.19.1737

Information

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

zbMATH: 1318.53097
MathSciNet: MR3352248
Digital Object Identifier: 10.2140/gt.2015.19.1737

Subjects:
Primary: 53D30

Rights: Copyright © 2015 Mathematical Sciences Publishers

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Vol.19 • No. 3 • 2015
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