The algebraic topology of Bloch points

Open theoretical problems concerning Bloch points still impede progress in magnetic bubble technology. The author attempts to show why the main approaches to understanding Bloch points are equivalent and have their formal justification in the Hopf extension theorem of algebraic topology. Specifically, E. Feldtkeller's (1965) S/sup 2/ winding number, J.C. Slonzcewski's (1979) gyrovector integral, and the usual topological charge associated with the Heisenberg ferromagnet are seen to be equivalent ways of calculating the degrees of a map into the order parameter space S/sup 2/. This approach is used to clarify the topological constraints which are respected in Bloch point creation and annihilation. The author concludes with some difficult open problems for which the topological approach needs to be supplemented by energetics and numerical simulation.>