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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The complex symplectic geometry of the deformation space of complex projective structures

Brice Loustau

Geometry & Topology 19 (2015) 1737–1775
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.

Keywords
complex projective structures, symplectic structures, Teichmüller theory, character variety, quasifuchsian structures
Mathematical Subject Classification 2010
Primary: 53D30
References
Publication
Received: 25 June 2014
Accepted: 9 January 2015
Published: 21 May 2015
Proposed: Jean-Pierre Otal
Seconded: Yasha Eliashberg, Ronald Stern
Authors
Brice Loustau
Département de Mathématiques
Université Paris-Sud
Bâtiment 425
Faculté des Sciences d’Orsay
91405 Orsay Cedex
France
http://www.math.u-psud.fr/~loustau/