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Călugăreanu Theorem

Letting Lk be the linking number of the two components of a ribbon, Tw be the twist, and Wr be the writhe, then

Lk(K)=Tw(K)+Wr(K).

(Adams 1994, p. 187).

See also

Gauss Integral, Linking Number, Twist, Writhe

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References

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, 1994.Călugăreanu, G. "L'intégrale de Gauss et l'Analyse des nœuds tridimensionnels." Rev. Math. Pures Appl. 4, 5-20, 1959.Călugăreanu, G. "Sur les classes d'isotopie des noeuds tridimensionnels et leurs invariants." Czech. Math. J. 11, 588-625, 1961.Călugăreanu, G. "Sur les enlacements tridimensionnels des courbes fermées." Comm. Acad. R. P. Romîne 11, 829-832, 1961.Kaul, R. K. "Topological Quantum Field Theories--A Meeting Ground for Physicists and Mathematicians." 15 Jul 1999. http://arxiv.org/abs/hep-th/9907119.Pohl, W. F. "The Self-Linking Number of a Closed Space Curve." J. Math. Mech. 17, 975-985, 1968.

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Călugăreanu Theorem

Cite this as:

Weisstein, Eric W. "Călugăreanu Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CalugareanuTheorem.html

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