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arXiv · 1103.2138

G2-instantons over Kovalev manifolds II

Henrique N. Sá Earp
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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.

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Henrique N. Sá Earp. 2014-01-28. G2-instantons over Kovalev manifolds II. https://arxiv.org/abs/1103.2138

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