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

Loustau, Brice

doi:10.2140/gt.2015.19.1737

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

Brice Loustau

Geometry & Topology 19 (2015) 1737–1775

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.

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/

Volume 19, issue 3 (2015)