  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.
