Topological Features in the Emerging Solar Magnetic Flux

The formation of highly structured, spatially localized complex structures during solar flux emergence facilitates adaptation of topological methods, extending the research of emerging macroscopic MHD fluxes into knots, links and braids. Combining mathematical considerations, remote images and in situ satellite observations at solar vicinity, we construct new characteristics of those braided/knotted magnetic structures, applying Braid and Knot Theory to physical configurations, deducing their topological invariants, constraining the evolution and stability while delineating the relaxation path to magnetized equilibria.