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The momentum map in Poisson geometry

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      Abstract

      Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in reduction.

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      Most cited references 14

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      Convexity properties of the moment mapping

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        Reduction of symplectic manifolds with symmetry

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          Integrability of Poisson Brackets

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            Author and article information

            Journal
            04 May 2007
            2009-03-02
            0705.0562

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            53D17; 53D20
            34 pages; to appear in American Journal of Mathematics
            math.SG math.DG

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