Stein, Jakob Richard;
(2022)
Gauge theory in co-homogeneity one.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
We use co-homogeneity one symmetries to construct new families of instantons over Riemannian manifolds with special holonomy groups and asymptotically conical geometry. In doing so, we give a complete description of the behaviour of Calabi-Yau instantons and monopoles with an SU(2)²-symmetry, by considering gauge theory on the smoothing and small resolution of the conifold, and on the canonical bundle of CP¹×CP¹, with their known asymptotically conical co-homogeneity one Calabi-Yau metrics. Furthermore, we classify SU(2)³-invariant G₂-instantons on the spinor bundle of the 3-sphere, equipped with the asymptotically conical co-homogeneity one G₂-metrics of Bryant-Salamon, and show that if any non-invariant instanton shares the same asymptotic behaviour, its deformation theory must be obstructed.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Gauge theory in co-homogeneity one |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10161752 |
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