Topology of symplectic torus actions with symplectic orbits
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- Duistermaat, J.J. & Pelayo, A. Rev Mat Complut (2011) 24: 59. doi:10.1007/s13163-010-0028-5
We give a concise overview of the classification theory of symplectic manifolds equipped with torus actions for which the orbits are symplectic (this is equivalent to the existence of a symplectic principal orbit), and apply this theory to study the structure of the leaf space induced by the action. In particular we show that if M is a symplectic manifold on which a torus T acts effectively with symplectic orbits, then the leaf space M/T is a very good orbifold with first Betti number b1(M/T)=b1(M)−dim T.