Writhe

Also called the Twist Number. The sum of crossings $p$ of a Link $L$,

$$w(L)=\sum_{p\in C(L)} \epsilon(p),$$

where $\epsilon(p)$ defined to be $\pm 1$ if the overpass slants from top left to bottom right or bottom left to top right and $C(L)$ is the set of crossings of an oriented Link. If a Knot $K$ is Amphichiral, then $w(K)=0$ (Thistlethwaite). Letting Lk be the Linking Number of the two components of a ribbon, Tw be the Twist, and Wr be the writhe, then

$$\mathop{\rm Lk}(K)=\mathop{\rm Tw}(K)+\mathop{\rm Wr}(K).$$

(Adams 1994, p. 187).

See also Screw, Twist

References

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, 1994.