Journal of Symplectic Geometry

Volume 12 (2014)

Number 2

Removal of singularities and Gromov compactness for symplectic vortices

Pages: 257 – 311

DOI: http://dx.doi.org/10.4310/JSG.2014.v12.n2.a3

Author

Andreas Ott (Centre for Mathematical Sciences, University of Cambridge, United Kingdom)

Abstract

We prove that the moduli space of gauge equivalence classes of symplectic vortices with uniformly bounded energy in a compact Hamiltonian manifold admits a Gromov compactification by polystable vortices. This extends results of Mundet i Riera for circle actions to the case of arbitrary compact Lie groups. Our argument relies on an a priori estimate for vortices that allows us to apply techniques used by McDuff and Salamon in their proof of Gromov compactness for pseudoholomorphic curves. As an intermediate result we prove a removable singularity theorem for symplectic vortices.

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