3D Measuring Surface: Hopfions

This chapter makes a further generalization: Instead of a 1D measuring path or a 2D measuring surface, it characterizes topological features using a 3D measuring space. The 3D measuring space leads to a 3D topological charge, called the Hopf index, which describes the linking of preimages in the orientational order. Based on this 3D topological charge, the chapter discusses hopfions as a new type of topological solitons.