$G_2$-Instantons on the Spinor Bundle of the 3-Sphere

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发表日期：

2024年3月27日

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Jakob Stein,
Matt Turner

摘要

We classify $G_2$ $G_{2}$ -instantons admitting $SU (2)^3$ $S U {(2)}^{3}$ -symmetries, and construct a new family of examples on the spinor bundle of the 3-sphere, equipped with the asymptotically conical, co-homogeneity one $G_2$ $G_{2}$ -metric of Bryant–Salamon. We also show that outside of the $SU (2)^3$ $S U {(2)}^{3}$ -invariant examples, any other $G_2$ $G_{2}$ -instanton on this metric with the same asymptotic behaviour must have obstructed deformations.

\(G_2\)-Instantons on the Spinor Bundle of the 3-Sphere

摘要