G2-instantons on generalised Kummer constructions. I

Details G2-instantons on generalised Kummer constructions. I G2-instantons on generalised Kummer constructions. I

2011-09-29

arxiv.org/abs/1109.6609v2

Mathematics

Differential Geometry

24 pages; some typos fixed, exposition improved

Scientific paper

In this article we introduce a method to construct G2-instantons on G2-manifolds arising from Joyce's generalised Kummer construction [Joy96]. The method is based on gluing anti-self-dual instantons on ALE spaces to flat bundles on G2-orbifolds of the form T^7/{\Gamma}. We give explicit examples of our construction. Finally we discuss the relevance of our work to the computation of a conjectural G2-instanton counting invariant as well as potential future applications.

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