Monopoles in higher dimensions

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Title: Monopoles in higher dimensions
Author(s): Marques Fernandes Oliveira, Goncalo
Item Type: Thesis or dissertation
Abstract: 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.
Content Version: Open Access
Publication Date: May-2014
Date Awarded: Aug-2014
Advisor: Donaldson, Simon
Sponsor/Funder: Fundacao para a Ciencia e a Tecnologia
Funder's Grant Number: SFRH / BD / 68756 / 2010
Department: Mathematics
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Mathematics PhD theses

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