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Examples of singularity models for $mathbb{Z}/2$ harmonic 1-forms and spinors in dimension 3

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 Added by Clifford H. Taubes
 Publication date 2020
  fields
and research's language is English




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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.



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