In this paper we suggest a soluiton to this question Does the existence of any nontrivially knotted closed trajectory for a field presents a positive lower bound for the energy and hence blocks the relaxation of the field into arbitrarily small energies

The classical Hopf invariant distinguishes among the homotopy classes of continuous mappings from the three-sphere to the two-sphere and is equal to the linking number of the two curves that are the… Expand

A group theoretical approach to hydrodynamics considers hydrodynamics to be the differential geometry of diffeomorphism groups. The principle of least action implies that the motion of a fluid is… Expand

Preface. Photograph of H.K. Moffatt. I: Eight Problems for the XXI Century. Some Remarks on Topological Fluid Mechanics H.K. Moffatt. II: Mathematics Background. Differential Geometry of Curves and… Expand

These notes are preliminary and informal. My aim is to provide an introduction to some of the basic ideas that have emerged in recent decades in the fluids literature that have a fundamentally… Expand