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Vortex invariants and toric manifolds

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arxiv 0812.0299 v1 pith:CI5JTDIN submitted 2008-12-01 math.SG

Jan Wehrheim This is my paper · ORCID
classification math.SG
keywords vortexactionformulainvariantssymplectictorictorusallows
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We consider the symplectic vortex equations for a linear Hamiltonian torus action. We show that the associated genus zero moduli space itself is homotopic (in the sense of a homotopy of regular G-moduli problems) to a toric manifold with combinatorial data directly obtained from the original torus action. This allows to view the wall crossing formula of Cieliebak and Salamon for the computation of vortex invariants as a consequence of a generalized Jeffrey-Kirwan localization formula for integrals over symplectic quotients.

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  1. On the geometry of magnetic Skyrmions on thin films

    cond-mat.mes-hall 2019-08 conditional novelty 7.0 of 10

    A BPS model of magnetic skyrmions is extended to curved thin films, with exact solutions on spheres, cones, and cylinders and a resolved moduli space.

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