Linking Number

A link invariant defined for a two-component oriented link as the sum of  crossings and  crossing over all crossings between the two links divided by 2. For components  and ,

where  is the set of crossings of  with , and  is the sign of the crossing. The linking number of a splittable two-component link is always 0.

REFERENCES:

Kauffman, L. Knots and Physics. Teaneck, NJ: World Scientific, p. 19, 1991.

Pohl, W. F. "The Self-Linking Number of a Closed Space Curve." J. Math. Mech. 17, 975-985, 1968.

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 132-133, 1976.