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math.SG2007
Symplectic Group Actions and Covering Spaces
James Montaldi, Juan-Pablo Ortega
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…
math.SG2005
Symmetry and symplectic reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in symplectic reduction. The article recalls most the necessary prerequisites to understand the ma…
math.SG2003
The relation between local and global dual pairs
James Montaldi, Juan-Pablo Ortega, Tudor S. Ratiu
In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage fro…