G2-instantons over Kovalev manifolds II

Abstract

This is the first nontrivial construction to date of instantons over a compact manifold with holonomy exactly $G_2$. The HYM connections on asymptotically stable bundles over Kovalev's noncompact Calabi-Yau 3-folds, obtained in the first article, are glued compatibly with a twisted connected sum, to produce a $G_2-$instanton over the resulting compact 7-manifold. This is accomplished under a nondegeneracy acyclic assumption on the bundle `at infinity', which occurs e.g. over certain projective varieties $X_{22}$ in $\mathbb{C}{P}^{13}$ equipped with an asymptotically rigid bundle.

arXiv comment23 pages, 1 figure. IMPORTANT: certain parts of this article are *wrong*; it is entirely superceded by arXiv:1310.7933v1 [math.DG]