Knots And Energy

This paper mainly introduces the related content of energy of knots. nergy of knots plays an important role in discriminating the complexity of the knots , it`s a good tool for the internal Qutan Suoniu for the knots.Although strict sense, the energy of knot is not an ambient isotopy invariant, but if we only in "explore the the miniming energy of the same knot type" , it still has many effect. Because we have an important result: for any real number b ,there are only many knot type which can have b as upper bound for the e_j~i of it.We can see it from the facets for approximating classified knots.This paper starting point is emphatically resolve "calculation difficult" problem of the energy. But calculation difficult, difficult on the complex in the definition. So this paper is based on the original definition and nature, based on a preliminary understanding of the definition of the characterization of knot meaning of energy and on this basis,from the perspective of a relatively simple to construct a definition of energy of knot. In order to achieve consistent with the original literature definition, this paper is after several deliberation basis, verified and each get a new definition will have plenty of calculation, until that was defined reasonable.On the basis of new definition. This paper got "all the energy of knot is positive", and "the energy of knot is grainning, within the scope of the etic knot with the number of knot intersection increasingly larger ", "energy bounded "and many other partly with the original document consistent conclusion. According to the new definition we calculate all the energy of knots less than 7 for intersection number.Although this paper did not provide more fresh things, but will tell from the analysis, this paper provides a sense of a simple understanding, and the angle of energy of knot attempted to other subjects and branch brings benefits.