Topology of symplectic torus actions with symplectic orbits
Publication date
2011-01
Authors
Duistermaat, J
Pelayo, A.
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Supervisors
Document Type
Article
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Abstract
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
Keywords
Symplectic manifold, Torus action, Orbifold, Betti number, Lie group, Symplectic orbit, Distribution, Foliation
Citation
Duistermaat, J J & Pelayo, A 2011, 'Topology of symplectic torus actions with symplectic orbits', Revista matemática complutense, vol. 24, no. 1, pp. 59-81. https://doi.org/10.1007/s13163-010-0028-5