论文标题
$ g_2 $ -instantons在$ g_2 $ -orbifolds的分辨率上
$G_2$-instantons on resolutions of $G_2$-orbifolds
论文作者
论文摘要
我们解释了通过解决$ g_2 $ -orbifolds获得的流形的$ g_2 $ -instantons的结构。这包括$ G_2 $ -INSTANTONS的$ T^7/γ$的特殊情况。所需的成分是Orbifold上的$ G_2 $ -INSTANTON，以及在胶合结构中使用的单数Orbifold集合上的Fueter部分。在一般情况下，我们做出了一个非常限制的假设，即Fueter部分是刻有刚性的。在$ t^7/γ$的特殊情况下，改进了对无扭转$ G_2 $结构的控制，可以删除此假设。作为一个应用程序，我们在$ t^7/γ$的分辨率的最简单示例中构造了大量的$ g_2 $ -instantons，其中有数百个不同的示例。我们还构建了$ G_2 $ -INSTANTON的一个新示例（$（T^3 \ times \ text {k3}）/\ mathbb {z}^2_2 $。
We explain a construction of $G_2$-instantons on manifolds obtained by resolving $G_2$-orbifolds. This includes the case of $G_2$-instantons on resolutions of $T^7/Γ$ as a special case. The ingredients needed are a $G_2$-instanton on the orbifold and a Fueter section over the singular set of the orbifold which are used in a gluing construction. In the general case, we make the very restrictive assumption that the Fueter section is pointwise rigid. In the special case of resolutions of $T^7/Γ$, improved control over the torsion-free $G_2$-structure allows to remove this assumption. As an application, we construct a large number of $G_2$-instantons on the simplest example of a resolution of $T^7/Γ$ with hundreds of distinct ones among them. We also construct one new example of a $G_2$-instanton on the resolution of $(T^3 \times \text{K3})/\mathbb{Z}^2_2$.
