Deformations of symplectic structures by moment maps

Tomoya Nakamura

    Research output: Contribution to journalArticle

    Abstract

    We study deformations of symplectic structures on a smooth manifold M via the quasi-Poisson theory. We can deform a given symplectic structure ω with a Hamiltonian G-action to a new symplectic structure ωt parametrized by some element t in Λ2g. 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.

    Original languageEnglish
    Pages (from-to)63-84
    Number of pages22
    JournalJournal of Geometry and Symmetry in Physics
    Volume47
    DOIs
    Publication statusPublished - 2018 Jan 1

    Keywords

    • Deformation-equivalent
    • Poisson
    • Quasi-Poisson
    • Symplectic

    ASJC Scopus subject areas

    • Mathematical Physics
    • Geometry and Topology

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