A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices Over the Plane

ISBN-13: 9780821894729 / Angielski

Fabian Ziltener

Opis

Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold $(Momega)$. Conjecturally under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten theory of $(Momega)$ 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 $mathbb$. 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.

Spis treści

• 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