Constructs 1-parameter families of two-spinor Seiberg-Witten monopoles converging to generic Z2-harmonic spinors via gluing with a generalized alternating method to cancel infinite-dimensional obstructions.
The zero loci of Z/2 harmonic spinors in dimension 2, 3 and 4
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
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.
fields
math.DG 3verdicts
UNVERDICTED 3representative citing papers
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.
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.
citing papers explorer
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Gluing $\mathbb Z_2$-Harmonic Spinors and Seiberg-Witten Monopoles on 3-Manifolds
Constructs 1-parameter families of two-spinor Seiberg-Witten monopoles converging to generic Z2-harmonic spinors via gluing with a generalized alternating method to cancel infinite-dimensional obstructions.
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Deformation rigidity for Z/2 eigensections
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.