Volume 17, issue 4 (2013)

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

Thomas Walpuski

Geometry & Topology 17 (2013) 2345–2388
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.

Keywords
$\mathrm{G}_2$–manifolds, $\mathrm{G}_2$–instantons, gauge theory, gluing constructions
Mathematical Subject Classification 2010
Primary: 53C07
Secondary: 53C25, 53C38