Jason Lotay, Goncalo Oliveira
Published 2018-12-31Version 1
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.
Comments: To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"
$SU(2)^2$-invariant $G_2$-instantons
New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$
Deformed $G_2$-instantons on $\mathbb{R}^4 \times S^3$
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