Article

Revista Matemática Complutense

, Volume 24, Issue 1, pp 59-81

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Topology of symplectic torus actions with symplectic orbits

  • J. J. DuistermaatAffiliated withMathematisch Instituut, Universiteit Utrecht
  • , A. PelayoAffiliated withMathematics Department, University of California–Berkeley Email author 

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

Mathematics Subject Classification (2000)

53D35 53C10