Linking Number

A link invariant defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components alpha and beta,

 Lk(alpha,beta)=1/2sum_(p in alpha coproduct beta)epsilon(p),

where alpha coproduct beta is the set of crossings of alpha with beta, and epsilon(p) is the sign of the crossing. The linking number of a splittable two-component link is always 0.

See also

Călugăreanu Theorem, Gauss Integral, Jones Polynomial, Link, Twist, Writhe

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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.

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Linking Number

Cite this as:

Weisstein, Eric W. "Linking Number." From MathWorld--A Wolfram Web Resource.

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