Geometric and causal properties of the sub-Lorentzian Heisenberg group

A space-time current is a Federer-Fleming current in a Euclidean space with a distinguished time direction. These objects facilitate a geometric theory of dislocation motion introduced by T. Hudson and F. Rindler, and as such they have received recent attention in their own right. In this talk, we shall discuss a ‘space-time connectivity theorem’ for normal currents, obtained in collaboration with P. Bonicatto and F. Rindler, and compare it with both the analogous result for integral currents and the classical Federer-Fleming connectivity theorem. Along the way, we shall use the Hudson-Rindler theory to motivate the study of space-time currents in various contexts.