In this thesis, we consider the problem of constructing G
2-instantons on two types of asymptotically conical manifolds, namely the Bryant-Salamon S
3xR
4 and the infinite collection of manifolds M
m,n constructed by Foscolo, Haskins and Nordström. Some progress has been made with the former example by Clarke, Lotay and Oliveira, while nothing was known about the existence of such instantons on the manifolds M
m,n. We firstly construct a 1-parameter family of instantons on the Bryant-Salamon S
3xR
4, and hence complete the picture of all invariant instantons on this manifold. Secondly, we construct a 1-parameter family of instantons on M
1,1 via a dynamical systems argument. Further, we consider an existence question of G
2-instantons on S
3xR
4 with an asymptotically locally conical metric, known as the BGGG metric. Again, some progress has been made in understanding the existence of such instantons on this manifold by Lotay and Oliveira, but there is still a region of initial conditions for which the existence of global solutions was previously unknown. We prove the existence of a boundary of initial conditions running through this unknown region and hence fully characterise the asymptotic behaviour of all complete bounded G
2-instantons on a specific bundle over this manifold.
- Gauge theory
- Special Holonomy
- Instantons
Gauge Theory on Manifolds with Conical Asymptotic Geometry
Turner, M. (Author). 29 Mar 2023
Student thesis: Doctoral Thesis › PhD