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2018 Deformations of Symplectic Structures by Moment Maps
Tomoya Nakamura
J. Geom. Symmetry Phys. 47(none): 63-84 (2018). DOI: 10.7546/jgsp-47-2018-63-84

Abstract

We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. We can deform a given symplectic structure $\omega $ with a Hamiltonian $G$-action to a new symplectic structure $\omega ^t$ parametrized by some element $t$ in $\Lambda^2\mathfrak{g}$. We can obtain concrete examples for the deformations of symplectic structures on the complex projective space and the complex Grassmannian. Moreover applying the deformation method to any symplectic toric manifold, we show that manifolds before and after deformations are isomorphic as a symplectic toric manifold.

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Tomoya Nakamura. "Deformations of Symplectic Structures by Moment Maps." J. Geom. Symmetry Phys. 47 63 - 84, 2018. https://doi.org/10.7546/jgsp-47-2018-63-84

Information

Published: 2018
First available in Project Euclid: 10 May 2018

zbMATH: 06944467
MathSciNet: MR3822061
Digital Object Identifier: 10.7546/jgsp-47-2018-63-84

Rights: Copyright © 2018 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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