Memoirs of the American Mathematical Society 2014; 129 pp; softcover Volume: 230 ISBN10: 0821894722 ISBN13: 9780821894729 List Price: US$76 Individual Members: US$45.60 Institutional Members: US$60.80 Order Code: MEMO/230/1082
 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 GromovWitten theory of \((M,\omega)\) to the GromovWitten 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  Motivation and main results
 Bubbling for vortices over the plane
 Fredholm theory for vortices over the plane
 Appendix A. Auxiliary results about vortices, weighted spaces, and other topics
 Bibliography
