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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:650697 |
| Date | January 2014 |
| Creators | Marques Fernandes Oliveira, Goncalo |
| Contributors | Donaldson, Simon |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/23570 |
Page generated in 0.0025 seconds