Title: $G_2$-instantons on the ALC members of the $\mathbb{B}_7$ family Show Chinese title

Title: $G_2$-在$\mathbb{B}_7$家族的 ALC 成员上的瞬子

Abstract: Using co-homogeneity one symmetries, we construct a two-parameter family of non-abelian $G_2$-instantons on every member of the asymptotically locally conical $\mathbb{B}_7$-family of $G_2$-metrics on $S^3 \times \mathbb{R}^4 $, and classify the resulting solutions. These solutions can be described as perturbations of a one-parameter family of abelian instantons, arising from the Killing vector-field generating the asymptotic circle fibre. Generically, these perturbations decay exponentially to the model, but we find a one-parameter family of instantons with polynomial decay. Moreover, we relate the two-parameter family to a lift of an explicit two-parameter family of anti-self-dual instantons on Taub-NUT $\mathbb{R}^4$, fibred over $S^3$ in an adiabatic limit. Show Chinese abstract

Abstract: 使用共齐次性对称性，我们在每个渐近局部圆锥形$\mathbb{B}_7$-族的$G_2$-度量 on$S^3 \times \mathbb{R}^4 $上构造了一个两参数的非阿贝尔$G_2$-瞬子族，并分类了所得解。 这些解可以描述为从生成渐近圆周纤维的 Killing 向量场产生的单参数阿贝尔瞬子族的扰动。 通常情况下，这些扰动会指数衰减到模型，但我们发现了一个具有多项式衰减的单参数瞬子族。 此外，我们将两参数族与 Taub-NUT$\mathbb{R}^4$上一个显式两参数的自对偶瞬子族在绝热极限下的提升相关联，该瞬子族纤维化在$S^3$上。