Abstract
AbstractWe show that the symplectic contraction map of Hilgert–Manon–Martens [9], a symplectic version of Popov’s horospherical contraction, is simply the quotient of a Hamiltonian manifold $M$ by a “stratified null foliation” that is determined by the group action and moment map. We also show that the quotient differential structure on the symplectic contraction of $M$ supports a Poisson bracket. We end by proving a very general description of the topology of fibers of Gelfand–Zeitlin (also spelled Gelfand–Tsetlin or Gelfand–Cetlin) systems on multiplicity-free Hamiltonian $U(n)$ and $SO(n)$ manifolds.
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