The Bogomolnyi equation is a PDE for a connection and a Higgs field on a bundle over a 3 dimensional Riemannian manifold. Possible extensions of this PDE to higher dimensions preserving the ellipticity modulo gauge transformations require some extra structure, which is available both in 6 dimensional Calabi-Yau manifolds and 7 dimensional G2 manifolds. These extensions are known as higher dimensional monopole equations and Donaldson and Segal proposed that “counting” solutions (monopoles) may give invariants of certain noncompact Calabi-Yau or G2 manifolds. In this thesis this possibility is investigated and examples of monopoles are constructed on certain Calabi-Yau and G2 manifolds. Moreover, this thesis also develops a Fredholm setup and
a moduli theory for monopoles on asymptotically conical manifolds.Open Acces
