The energy spectrum of knots and links

摘要: KNOTTED and linked structures arise in such disparate fields as plasma physics, polymer molecular biology cosmic string theory. It is important to be able characterize classify structures. Early attempts do so1 were stimulated by Kelvin's2 recognition of the invariance knotted vortex tubes fluid flow governed classical Euler equations motion. The techniques mechanics are still very natural for investigation certain problems that essentially topological character. Here I use these establish existence a new type invariant knots links. Any knot or link may characterized an 'energy spectrum'—a set positive real numbers determined solely its topology. lowest energy provides possible measure complexity.