${\rm G}_2$-instantons on generalised Kummer constructions

Thomas Walpuski

arXiv:1109.6609·math.DG·November 11, 2014

${\rm G}_2$-instantons on generalised Kummer constructions

Thomas Walpuski

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TL;DR

This paper presents a new method for constructing G2-instantons on G2-manifolds derived from Joyce's generalized Kummer construction, expanding the set of known solutions in this geometric context.

Contribution

It introduces a gluing technique combining ASD instantons on ALE spaces with flat bundles on G2-orbifolds, providing explicit non-trivial G2-instanton examples.

Findings

01

Constructed new G2-instantons on Joyce's G2-manifolds.

02

Demonstrated the effectiveness of the gluing method.

03

Produced explicit examples of non-trivial G2-instantons.

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 $T^{7} /Γ$ . We use this construction to produce non-trivial examples of $G_{2}$ -instantons.

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