Symplectic group actions and covering spaces

James Montaldi, Juan Pablo Ortega

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    For symplectic group actions which are not Hamiltonian there are two ways to define reduction. Firstly using the cylinder-valued momentum map and secondly lifting the action to any Hamiltonian cover (such as the universal cover), and then performing symplectic reduction in the usual way. We show that provided the action is free and proper, and the Hamiltonian holonomy associated to the action is closed, the natural projection from the latter to the former is a symplectic cover. At the same time we give a classification of all Hamiltonian covers of a given symplectic group action. The main properties of the lifting of a group action to a cover are studied. © 2009 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)589-604
    Number of pages15
    JournalDifferential Geometry and its Application
    Issue number5
    Publication statusPublished - Oct 2009


    • Hamiltonian holonomy
    • Lifted group action
    • Momentum map
    • Symplectic reduction
    • Universal cover


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