Monopoles on R⁵
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 describ...
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University of Leeds
2015
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ndltd-bl.uk-oai-ethos.bl.uk-6852362017-10-04T03:32:48ZMonopoles on R⁵Pires dos Santos, RodrigoSpeight, Martin2015This 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.516.3University of Leedshttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.685236http://etheses.whiterose.ac.uk/12561/Electronic Thesis or Dissertation |
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516.3 |
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516.3 Pires dos Santos, Rodrigo Monopoles on R⁵ |
| description |
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. |
| author2 |
Speight, Martin |
| author_facet |
Speight, Martin Pires dos Santos, Rodrigo |
| author |
Pires dos Santos, Rodrigo |
| author_sort |
Pires dos Santos, Rodrigo |
| title |
Monopoles on R⁵ |
| title_short |
Monopoles on R⁵ |
| title_full |
Monopoles on R⁵ |
| title_fullStr |
Monopoles on R⁵ |
| title_full_unstemmed |
Monopoles on R⁵ |
| title_sort |
monopoles on r⁵ |
| publisher |
University of Leeds |
| publishDate |
2015 |
| url |
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.685236 |
| work_keys_str_mv |
AT piresdossantosrodrigo monopolesonr5 |
| _version_ |
1718544938051829760 |