Monopoles on 3 dimensional AC manifolds

Abstract

We construct monopoles in any asymptotically conical (AC) $3$-manifold $X$ with $b^2(X)=0$. For sufficiently large mass, our construction covers an open set in the moduli space of monopoles. We also give a more general construction of Dirac monopoles in any AC manifold, which may be useful for generalizing our result to the case when $b^2(X)\ne 0$.

Definition of moduli changed in order to directly use the results in one of the key references. Exposition improved

References in corpus (1)

• Dimension of monopoles on asymptotically conic 3-manifolds

Cited by in corpus (5)

• The limit of large mass monopoles
• Deformation of singular connections I: $G_2-$instantons with point singularities
• A gluing construction for periodic monopoles
• The Haydys monopole equation
• Local solution to the $G_2-$monopole equation with prescribed tangent cone and $G_2-$structure