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

Loustau, Brice¹

¹ Département de Mathématiques, Université Paris-Sud, Bâtiment 425, Faculté des Sciences d’Orsay, 91405 Orsay Cedex, France

Geometry & topology, Tome 19 (2015) no. 3, pp. 1737-1775.

Résumé

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.

Détail

DOI : 10.2140/gt.2015.19.1737

Classification : 53D30
Keywords: complex projective structures, symplectic structures, Teichmüller theory, character variety, quasifuchsian structures

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