Deformations of Symplectic Structures by Moment Maps

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.