G₂-instantons on Resolutions of G₂-orbifolds

We explain a construction of G₂ G2 -instantons on manifolds obtained by resolving G₂ G2 -orbifolds. This includes the case of G₂ G2 -instantons on resolutions of T⁷/Γ T7/Γ as a special case. The ingredients needed are a G₂ G2 -instanton on the orbifold and a Fueter section over the singular set of the orbifold which are used in a gluing construction. In the general case, we make the very restrictive assumption that the Fueter section is pointwise rigid. In the special case of resolutions of T⁷/Γ T7/Γ , improved control over the torsion-free G₂ G2 -structure allows to remove this assumption. As an application, we construct a large number of G₂ G2 -instantons on the simplest example of a resolution of T⁷/Γ T7/Γ . We also construct one new example of a G₂ G2 -instanton on the resolution of (T³ × K3)/Z²₂ (T3×K3)/Z22 .