Dimension of monopoles on asymptotically conic 3-manifolds

Abstract

The virtual dimensions of both framed and unframed SU(2) magnetic monopoles on asymptotically conic 3-manifolds are obtained by computing the index of a Fredholm extension of the associated deformation complex. The unframed dimension coincides with the one obtained by Braam for conformally compact 3-manifolds. The computation follows from the application of a Callias-type index theorem.

18 pages. New revision computes both framed and unframed moduli dimensions, incorporates referee suggestions

References in corpus (2)

• A Callias-type index theorem with degenerate potentials
• Monopoles on the Bryant-Salamon $G_2$ Manifolds

Cited by in corpus (4)

• A Callias-type index theorem with degenerate potentials
• Monopoles on 3 dimensional AC manifolds
• The limit of large mass monopoles
• A hyper-Kähler metric on the moduli spaces of monopoles with arbitrary symmetry breaking