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A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane
 
Fabian Ziltener Korea Institute for Advanced Study, Seoul, Republic of Korea
A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane
eBook ISBN:  978-1-4704-1672-0
Product Code:  MEMO/230/1082.E
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $45.60
A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane
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A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane
Fabian Ziltener Korea Institute for Advanced Study, Seoul, Republic of Korea
eBook ISBN:  978-1-4704-1672-0
Product Code:  MEMO/230/1082.E
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $45.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2302014; 129 pp
    MSC: Primary 58; 53;

    Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold \((M,\omega)\). Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten theory of \((M,\omega)\) to the Gromov-Witten theory of the symplectic quotient. The morphism should be a deformation of the Kirwan map. The idea, due to D. A. Salamon, is to define such a deformation by counting gauge equivalence classes of symplectic vortices over the complex plane \(\mathbb{C}\).

    The present memoir is part of a project whose goal is to make this definition rigorous. Its main results deal with the symplectically aspherical case.

  • Table of Contents
     
     
    • Chapters
    • 1. Motivation and main results
    • 2. Bubbling for vortices over the plane
    • 3. Fredholm theory for vortices over the plane
    • A. Auxiliary results about vortices, weighted spaces, and other topics
  • 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: 2302014; 129 pp
MSC: Primary 58; 53;

Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold \((M,\omega)\). Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten theory of \((M,\omega)\) to the Gromov-Witten theory of the symplectic quotient. The morphism should be a deformation of the Kirwan map. The idea, due to D. A. Salamon, is to define such a deformation by counting gauge equivalence classes of symplectic vortices over the complex plane \(\mathbb{C}\).

The present memoir is part of a project whose goal is to make this definition rigorous. Its main results deal with the symplectically aspherical case.

  • Chapters
  • 1. Motivation and main results
  • 2. Bubbling for vortices over the plane
  • 3. Fredholm theory for vortices over the plane
  • A. Auxiliary results about vortices, weighted spaces, and other topics
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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