G2-instantons over Kovalev manifolds II

Details G2-instantons over Kovalev manifolds II G2-instantons over Kovalev manifolds II

2011-03-10

arxiv.org/abs/1103.2138v1

Mathematics

Differential Geometry

23 pages, 1 figure

Scientific paper

This is the first nontrivial construction to date of instantons over a compact manifold with holonomy exactly G2. 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 G2-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 CP^13 equipped with an asymptotically rigid bundle.

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