论文标题
$ \ mathbb {z}/2 $谐波1形和旋转器中的奇异模型的示例
Examples of singularity models for $\mathbb{Z}/2$ harmonic 1-forms and spinors in dimension 3
论文作者
论文摘要
我们使用四面体，八面体和二十面体的对称性来构建$ \ mathbb {z}/2 $谐波1型或旋转器的本地模型，或者在其零基因座的单数点附近的3维中旋转。本地型号为$ \ mathbb {z}/2 $谐波1型或在$ \ mathbb {r}^3 $上的旋转器，对于$ \ mathbb {r}^3 $的重新续订而言，它们的零位点由四个或更多的射线组成。在一个示例中，射线从原点到一个中心四面体的顶点。他们指出的是，在两个中心的八面体和另外两个中心的Icosahedron。
We use the symmetries of the tetrahedron, octahedron and icosahedron to construct local models for a $\mathbb{Z}/2$ harmonic 1-form or spinor in 3-dimensions near a singular point in its zero loci. The local models are $\mathbb{Z}/2$ harmonic 1-forms or spinors on $\mathbb{R}^3$ that are homogeneous with respect to rescaling of $\mathbb{R}^3$ with their zero locus consisting of four or more rays from the origin. The rays point from the origin to the vertices of a centered tetrahedron in one example; and they point from those of a centered octahedron and a centered icosahedron in two others.
