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2006 On the First Pontryagin Form of a Surface
Roberto Ferreiro Pérez, Jaime Muňoz Masqué
J. Geom. Symmetry Phys. 5: 75-81 (2006). DOI: 10.7546/jgsp-5-2006-75-81


The first Pontryagin form of a compact orientable surface $M$ determines a canonical pre-symplectic structure on the space of Riemannian metrics on $M$. The first equivariant Pontryagin form determines a canonical moment map for it. We study the corresponding symplectic reduction and we state (Theorem 6) that the symplectic quotient is the Teichmüller space of the surface with the Weil-Petersson symplectic form.


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Roberto Ferreiro Pérez. Jaime Muňoz Masqué. "On the First Pontryagin Form of a Surface." J. Geom. Symmetry Phys. 5 75 - 81, 2006.


Published: 2006
First available in Project Euclid: 20 May 2017

zbMATH: 1105.53064
MathSciNet: MR2269881
Digital Object Identifier: 10.7546/jgsp-5-2006-75-81

Rights: Copyright © 2006 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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