Bowline more resistant to jamming than the other variations, especially when wet. In this variation the knot's working end is taken round the loop in the direction of the original round turn, then threaded back up through the original round turn before the knot is drawn tight. The Yosemite bowline is often used in climbing. The cowboy bowline (also called Dutch bowline), French bowline, and Portuguese bowline are variations of the bowline, each of which makes one loop. (Names of knots are mostly traditional and may not reflect their origins.) A running bowline can be used to make a noose which
Arf invariant of a knot the knot, constructed from a set of curves on a Seifert surface of genus "g" which represent a basis for the first homology of the surface. This means that "V" is a 2"g" × 2"g" matrix with the property that "V" − "V" is a symplectic matrix. The "Arf invariant" of the knot is the residue of Specifically, if formula_3, is a symplectic basis for the intersection form on the Seifert surface, then where formula_5 denotes the positive pushoff of "a". This approach to the Arf invariant is due to Louis Kauffman. We define two knots to be pass equivalent