A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane
Author： Fabian Ziltener
Publisher： American Mathematical Society
Publication year： 2014
E-ISBN: 9781470416720
P-ISBN(Paperback): 9780821894729
P-ISBN(Hardback): 9780821894729
Subject： O186 Differential Geometry and Integral Geometry
Keyword： Geometry and Topology
Language： ENG
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A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane
Description
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 Gromov-Witten theory of $(M,\omega)$ 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 $\mathbb{C}$. 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.