Dynamics of topological magnetic solitons

A direct link between the topological complexity of magnetic media and thei r dynamics is established through the construction of unambiguous conservat ion laws for the linear and angular momenta as moments of a topological vor ticity. As a consequence, the dynamics of topological magnetic solitons is shown to exhibit the characteristic features of the Hall effect of electrod ynamics or the Magnus effect of fluid dynamics. The main points of this pro gram are reviewed here for both ferromagnets and antiferromagnets, while a straightforward extension to the study of superfluids is also discussed bri efly.