Gauge Theory on Manifolds with Conical Asymptotic Geometry

  • Matthew Turner

Student thesis: Doctoral ThesisPhD


In this thesis, we consider the problem of constructing G2-instantons on two types of asymptotically conical manifolds, namely the Bryant-Salamon S3xR4 and the infinite collection of manifolds Mm,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 Mm,n. We firstly construct a 1-parameter family of instantons on the Bryant-Salamon S3xR4, and hence complete the picture of all invariant instantons on this manifold. Secondly, we construct a 1-parameter family of instantons on M1,1 via a dynamical systems argument. Further, we consider an existence question of G2-instantons on S3xR4 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 G2-instantons on a specific bundle over this manifold.
Date of Award29 Mar 2023
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorJohannes Nordstrom (Supervisor) & Karsten Matthies (Supervisor)


  • Gauge theory
  • Special Holonomy
  • Instantons

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