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Title: Monopoles in higher dimensions
Author: Marques Fernandes Oliveira, Goncalo
ISNI:       0000 0004 5357 0664
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2014
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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.
Supervisor: Donaldson, Simon Sponsor: Fundacao para a Ciencia e a Tecnologia
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available