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Symplectic Actions of $2$-Tori on $4$-Manifolds
 
Alvaro Pelayo University of California at Berkeley, Berkeley, CA
Symplectic Actions of $2$-Tori on $4$-Manifolds
eBook ISBN:  978-1-4704-0573-1
Product Code:  MEMO/204/959.E
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
Symplectic Actions of $2$-Tori on $4$-Manifolds
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Symplectic Actions of $2$-Tori on $4$-Manifolds
Alvaro Pelayo University of California at Berkeley, Berkeley, CA
eBook ISBN:  978-1-4704-0573-1
Product Code:  MEMO/204/959.E
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2042009; 81 pp
    MSC: Primary 53; Secondary 57; 55;

    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
     
     
    • Chapters
    • Acknowledgements
    • 1. Introduction
    • 2. The orbit space
    • 3. Global model
    • 4. Global model up to equivariant diffeomorphisms
    • 5. Classification: Free case
    • 6. Orbifold homology and geometric mappings
    • 7. Classification
    • 8. The four-dimensional classification
    • 9. Appendix: (sometimes symplectic) orbifolds
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2042009; 81 pp
MSC: Primary 53; Secondary 57; 55;

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.

  • Chapters
  • Acknowledgements
  • 1. Introduction
  • 2. The orbit space
  • 3. Global model
  • 4. Global model up to equivariant diffeomorphisms
  • 5. Classification: Free case
  • 6. Orbifold homology and geometric mappings
  • 7. Classification
  • 8. The four-dimensional classification
  • 9. Appendix: (sometimes symplectic) orbifolds
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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