Monopoles in higher dimensions
Author(s)
Marques Fernandes Oliveira, Goncalo
Type
Thesis
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.
a moduli theory for monopoles on asymptotically conical manifolds.
Version
Open Access
Date Issued
2014-05
Date Awarded
2014-08
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Donaldson, Simon
Sponsor
Fundacao para a Ciencia e a Tecnologia
Grant Number
SFRH / BD / 68756 / 2010
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)