#### Volume 17, issue 4 (2013)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
$\mathrm{G}_2$–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