A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane (Memoirs of the American Mathematical Society)
By: Fabian Ziltener (author)Paperback
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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.
Fabian Ziltener, Korea Institute for Advanced Study, Seoul, Republic of Korea.
Motivation and main resultsBubbling for vortices over the planeFredholm theory for vortices over the planeAppendix A. Auxiliary results about vortices, weighted spaces, and other topicsBibliography
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- ID: 9780821894729
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