Torsion Cycles as Non-Local Magnetic Sources in Non-Orientable Spaces

Non-orientable spaces are known to be able to support net magnetic fluxes through closed surfaces, even in the absence of magnetic sources. To an observer for whom the non-orientability of space appears to be confined to a certain finite region of space, such a magnetic flux appears as a magnetic charge quasi-localised in that region. In this paper it is shown that this effect is a physical manifestation of the existence of torsion cycles of codimension one in the homology of space.