Topology bounds energy of knots and links

In this paper, we determine two quantities, of geometric and topological character, that were left undetermined in two previous results obtained by Arnold (Arnold 1974 In Proc. Summer School in Diff. Eqs. at Dilizhan , pp. 229–256.) and Moffatt (Moffatt 1990 Nature 347 , 367–369) on lower bounds for the magnetic energy of knots and links in ideal fluids. For dissipative systems, a lower bound on magnetic helicity in terms of the average crossing number and a new relationship between rates of change of these two quantities are also determined.