G2–instantons on generalised Kummer constructions

Walpuski, Thomas¹

¹ Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK

Geometry & topology, Tome 17 (2013) no. 4, pp. 2345-2388.

Résumé

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.

Détail

DOI : 10.2140/gt.2013.17.2345

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

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