2014/07/23 by Clifford Henry Taubes, Taubes, Clifford Henry · 8 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Geometric Analysis and Curvature Flows #math.DG #msc:53C07 #msc:57R57
paper · pdf · doi:10.48550/arxiv.1407.6206
This paper corrects and extends theorems in arXiv:1307.6451, arXiv:1307.6447 and arXiv:1205.0514
arxiv created 2014/07/23 · arxiv updated 2014/07/24
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.