White Rose University Consortium logo
University of Leeds logo University of Sheffield logo York University logo

Monopoles on R^5

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

PiresdosSantos_R_PhD_2015.pdf - Final eThesis - redacted (pdf)
Available under License Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales.

Download (514Kb) | Preview


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

You do not need to contact us to get a copy of this thesis. Please use the 'Download' link(s) above to get a copy.
You can contact us about this thesis. If you need to make a general enquiry, please see the Contact us page.

Actions (repository staff only: login required)