$\mathrm{G}_2$–instantons on generalised Kummer constructions

Abstract

In this article we introduce a method to construct $G_2$–instantons on $G_2$–manifolds arising from Joyce’s generalised Kummer construction. The method is based on gluing ASD instantons over ALE spaces to flat bundles on $G_2$–orbifolds of the form $T^7∕\Gamma$. We use this construction to produce non-trivial examples of $G_2$–instantons.