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- W1644003929 abstract "Consider a Hamiltonian action of a compact connected Lie group $G$ on an aspherical symplectic manifold $(M,omega)$. Under some assumptions on $(M,omega)$ and the action, D. A. Salamon conjectured that counting gauge equivalence classes of symplectic vortices on the plane $R^2$ gives rise to a quantum deformation $Qkappa_G$ of the Kirwan map. This article is the first of three, whose goal is to define $Qkappa_G$ rigorously. Its main result is that the vertical differential of the vortex equations over $R^2$ (at the level of gauge equivalence) is a Fredholm operator of a specified index. Potentially, the map $Qkappa_G$ can be used to compute the quantum cohomology of many symplectic quotients. Conjecturally it also gives rise to quantum generalizations of non-abelian localization and abelianization (see [Woodward-Ziltener])." @default.
- W1644003929 created "2016-06-24" @default.
- W1644003929 creator A5074786158 @default.
- W1644003929 date "2009-05-25" @default.
- W1644003929 modified "2023-09-27" @default.
- W1644003929 title "A Quantum Kirwan Map, I: Fredholm Theory" @default.
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