On Gauss' linking number and the energy spectrum of magnetic knots

By revisiting Gauss work on magnetism we provide [1] a plausible reconstructionof what might have been Gauss own derivation of the linking number
concept and formula. Information on linking number and crossing number are fundamental
in a topological approach to field theory, topology providing a lower bounds on the
energy of the physical system [2]. In the case of knots, for instance, an exact analytical
expression for the minimum energy is found and the energy spectrum determined [3].
These results are fundamental in the classification of knots and links by energy methods and in the search for ground-state energy information in topological field theory [4].



[1] Ricca, R.L., Nipoti, B. On the original derivation and modern interpretations of
Gauss' linking number. To be submitted to J. Knot Theory and Its Ram.


[2] Ricca (2008) Topology bounds energy of knots and links. Proc. R. Soc. A 464, 293-300.


[3] Maggioni, F. and Ricca, R.L. (2009) On the groundstate energy of tight knots. Proc. R. Soc. A 465, 2761-2783.


[4] Ricca, R.L. (Ed.) (2009) Lectures on Topological Fluid Mechanics. Springer-CIME
Lecture Notes in Mathematics 1973. Springer-Verlag. Heidelberg, Germany.