Revista Matemática Complutense

, Volume 24, Issue 1, pp 59–81

Topology of symplectic torus actions with symplectic orbits

Open AccessArticle

DOI: 10.1007/s13163-010-0028-5

Cite this article as:
Duistermaat, J.J. & Pelayo, A. Rev Mat Complut (2011) 24: 59. doi:10.1007/s13163-010-0028-5

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 manifoldTorus actionOrbifoldBetti numberLie groupSymplectic orbitDistributionFoliation

Mathematics Subject Classification (2000)

53D3553C10
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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands
  2. 2.Mathematics DepartmentUniversity of California–BerkeleyBerkeleyUSA