, Volume 24, Issue 1, pp 59-81,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 13 Mar 2010

Topology of symplectic torus actions with symplectic orbits

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.

A. Pelayo was partially supported by an NSF fellowship.