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Monopoles on R^5

Pires dos Santos, Rodrigo (2015) Monopoles on R^5. PhD thesis, University of Leeds.

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Abstract

This thesis is motived by the wish to understand the structure of the moduli space of monopoles on R^5. Our approach to define monopoles is twistorial and we start by developing the twistor theory of R^5, which is an analogue of the twistor theory for R^3 developed by Hitchin. Using this, we describe a Hitchin-Ward transform for R^5, giving monopoles for the group SU(2). In order for us to construct monopoles we make use of spectral curves. Then, using those spectral curves we find a new system of equations, analogue to the Nahm's equations. Lastly, we prove that the geometry of the moduli space of solutions to this Nahm's equations carries a 2-symplectic structure.

Item Type: Thesis (PhD)
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds)
The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Identification Number/EthosID: uk.bl.ethos.685236
Depositing User: Rodrigo Pires dos Santos
Date Deposited: 16 May 2016 10:35
Last Modified: 06 Oct 2016 14:42
URI: http://etheses.whiterose.ac.uk/id/eprint/12561

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