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arXiv · 1812.11867

$G_2$-instantons on noncompact $G_2$-manifolds: results and open problems

Jason Lotay·Goncalo Oliveira
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Abstract

We survey the known existence and non-existence results for $G_2$-instantons on non-compact cohomogeneity-1 $G_2$-manifolds and their consequences, including an explicit example of a family of $G_2$-instantons where bubbling, removable singularities and conservation of energy phenomena occur. We also describe several open problems for future research.

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Jason Lotay, Goncalo Oliveira. 2018-12-31. $G_2$-instantons on noncompact $G_2$-manifolds: results and open problems. https://arxiv.org/abs/1812.11867

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