Symplectic group actions and covering spaces

Montaldi, James and Ortega, Juan-Pablo (2009) Symplectic group actions and covering spaces. Differential Geometry and its Applications, 27 (2009). pp. 589-604.

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Abstract

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.

Item Type: Article
Additional Information: 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 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 51 Geometry (See also algebraic geometry)
Depositing User: Dr James Montaldi
Date Deposited: 19 Aug 2008
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1137

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