Summary and Info
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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