Energy of a Knot

Almost all energies are not homothety invariant, so we will consider only knots of length 2π. The energy of a knot is not an invariant of the topological class of this knot. If we make a smooth perturbation of a knot, its energy smoothly changes. We will consider energies with the following important properties. The energy is always positive. When a knot crossing tends to a double point, the energy tends to infinity. So every topological class of knots has a representative with the minimal value of energy. This knot is called a