The zero loci of Z/2 harmonic spinors in dimension 2, 3 and 4
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Supposing that X is a Riemannian manifold, a Z/2 spinor on X is defined by a data set consisting of a closed set in X to be denoted by Z, a real line bundle over X-Z, and a nowhere zero section on X-Z of the tensor product of the real line bundle and a spinor bundle. The set Z and the spinor are jointly constrained by the following requirement: The norm of the spinor must extend across Z as a continuous function vanishing on Z. In particular, the vanishing locus of the norm of the spinor is the complement of the set where the real line bundle is defined, and hence where the spinor is defined. The Z/2 spinor is said to be harmonic when it obeys a first order Dirac equation on X-Z. This monograph analyzes the structure of the set Z for a Z/2 harmonic spinor on a manifold of dimension either two, three or four.
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Cited by 3 Pith papers
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Every minimal non-degenerate critical Z/2 eigensection on S^2 is deformation rigid, so small changes to the branch-point configuration that preserve criticality must come from SO(3) rotations.
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Homogeneous $\mathbb Z/2$-Harmonic Forms and Spinors on $\mathbb{R}^4$ from Regular 4-Polytopes
Novel homogeneous singularity models for Z/2-harmonic forms and spinors on R^4 are built as cones on the 1-skeleta of regular 4-polytopes.
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