A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane
Author: Fabian Ziltener
Publisher: American Mathematical Soc.
Published: 2014-06-05
Total Pages: 142
ISBN-13: 0821894722
DOWNLOAD EBOOKConsider a Hamiltonian action of a compact connected Lie group on a symplectic manifold . Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten theory of 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 . 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.