2011/06/09 by Fabian Ziltener, Ziltener, Fabian · 1 citation
Mathematics · #53D20 #53D45 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D20 #msc:53D45
paper · pdf · doi:10.48550/arxiv.1106.1729
This article has been merged with arXiv:0905.4047. The new article is: A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane, arXiv:1209.5866
arxiv created 2012/09/27 · arxiv updated 2012/09/28
Consider a Hamiltonian action of a compact connected Lie group G on an aspherical symplectic manifold (M,ω). Under suitable assumptions, counting gauge equivalence classes of (symplectic) vortices on the plane R2 conjecturally gives rise to a quantum deformation QkG of the Kirwan map. This is the second of a series of articles, whose goal is to define QkG rigorously. The main result is that every sequence of vortices with uniformly bounded energies has a subsequence that converges to a genus 0 stable map of vortices on R2 and holomorphic spheres in the symplectic quotient. Potentially, the map QkG 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.