Partial compactification of monopoles and metric asymptotics

2015/12/09 by Chris Kottke, Kottke, Chris, Singer, Michael · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1512.02979

openalex publication_date 2015/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a partial compactification of the moduli space, M_k, of SU(2) magnetic monopoles on R³, wherein monopoles of charge k decompose into widely separated 'monopole clusters' of lower charge going off to infinity at comparable rates. The hyperKahler metric on M_k has a complete asymptotic expansion up to the boundary, the leading term of which generalizes the asymptotic metric discovered by Bielawski, Gibbons and Manton in the case that each lower charge is 1.

Cited by

• The large mass limit of monopoles: abelian limits and Dirac singularities
• Géométrie à l'infini des variétés hyperkählériennes toriques

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