Examples of singularity models for $\mathbb{Z}/2$ harmonic 1-forms and spinors in dimension 3
| Autor: | Taubes, Clifford Henry, Wu, Yingying |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Groups actions are corrected and more details are given about them. An appendix has been added proving that if Z has only 2 rays from the origin, then the rays are antipodal |
| Databáze: | arXiv |
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