The Geometric Structure of Symplectic Contraction
2018 ◽
Vol 2020
(12)
◽
pp. 3521-3539
◽
Keyword(s):
Abstract We 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.
1994 ◽
Vol 31
(2)
◽
pp. 185-191
◽
2003 ◽
Vol 50
(15-17)
◽
pp. 2691-2704
◽
2020 ◽
Vol 3
(2)
◽
pp. 109-119
1999 ◽
Vol 1
(4)
◽
pp. 351-370
◽
Keyword(s):