2007.84: Symplectic group actions and covering spaces
2007.84: James Montaldi and Juan-Pablo Ortega (2009) Symplectic group actions and covering spaces. Differential Geometry and its Applications, 27 (2009). pp. 589-604.
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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 covering. At the same time we give a classification of all Hamiltonian coverings of a given symplectic group action. The main properties of the lifting of a group action to a cover are studied.
Compared to previous versions, this latest version has a shortened section 1, and an added example.
|Uncontrolled Keywords:||lifted group action, symplectic reduction, universal covering, Hamiltonian holonomy, momentum map|
|Subjects:||MSC 2000 > 22 Topological groups, Lie groups|
MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 51 Geometry (See also algebraic geometry)
|Deposited By:||Dr James Montaldi|
|Deposited On:||19 August 2008|
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