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Quantum Kirwan map: bubbling and Fredholm theory for symplectic vortices over the plane / Fabian Ziltener.

By: Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 230, no 1082.Publication details: Providence : American Mathematical Society, c2014.Description: v, 129 p. : illustrations ; 26 cmISBN:
  • 9780821894729 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Motivation and main results -- 2. Bubbling for vortices over the plane -- 3. Fredholm theory for vortices over the plane -- Appendix A. Auxiliary results about vortices, weighted spaces, and other topics-- Bibliography.
Summary: Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold M ,w. Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten theory of M , w 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 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 135903
Total holds: 0

"July 2014, volume 230, number 1082 (fourth of 5 numbers)."

Includes bibliographical references (pages 127-129).

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

Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold M ,w. Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten theory of M , w 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 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.

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