Near Force-Free Magnetic Field Characterization via Contact Topology and Functorial Constructions

The Giroux correspondence can be used to obtain a topological characterization of near force-free magnetic fields. The present work exposes some finer algebraic structure of the resulting classification by appealing to category theory to organize the underlying calculations. In this way, certain highly nonconvex inverse problems in “topological electromagnetics” reveal structure that is appreciable in terms of analogies with other developed fields of engineering.