A topological invariant to predict the three-dimensional writhe of ideal configurations of knots and links

We present herein a topological invariant of oriented alternating knots and links that predicts the three-dimensional (3D) writhe of the ideal geometr ical configuration of the considered knot/link, The fact that we can correl ate a geometrical property of a given configuration with a topological inva riant supports the notion that the ideal configuration contains important i nformation about knots and links. The importance of the concept of ideal co nfiguration was already suggested by the good correlation between the 3D wr ithe of ideal knot configurations and the ensemble average of the 3D writhe of random configurations of the considered knots. The values of the new in variant are quantized: multiples of 4/7 for links with an odd number of com ponents (including knots) and 2/7 plus multiples of 4/7 for links with an e ven number of components.