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Symplectic Actions of \(2\)-Tori on \(4\)-Manifolds
Alvaro Pelayo, University of California at Berkeley, CA
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Memoirs of the American Mathematical Society
2009; 81 pp; softcover
Volume: 204
ISBN-10: 0-8218-4713-9
ISBN-13: 978-0-8218-4713-8
List Price: US$64
Individual Members: US$38.40
Institutional Members: US$51.20
Order Code: MEMO/204/959
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In this paper the author classifies symplectic actions of \(2\)-tori on compact connected symplectic \(4\)-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The classification is in terms of a collection of invariants of the topology of the manifold, of the torus action and of the symplectic form. The author constructs explicit models of such symplectic manifolds with torus actions, defined in terms of these invariants.

Table of Contents

  • Introduction
  • The orbit space
  • Global model
  • Global model up to equivariant diffeomorphisms
  • Classification: Free case
  • Orbifold homology and geometric mappings
  • Classification
  • The four-dimensional classification
  • Appendix: (sometimes symplectic) orbifolds
  • Bibliography
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