Yosemite bowline form a highly dangerous slip knot. Additional safety is achieved by tying with a tail (see below). When finished, the working end forms a figure eight. Because of the danger of incorrectly tying the Yosemite bowline, it may be safer and less error-prone to use a standard or double bowline with a backup stopper knot added to the tail, such as a double overhand knot tied around the loop. The Yosemite finish can be applied to other bowline variants, such as the double bowline. While the knot's versatility suggests it as a convenient tie-in for attaching a climbing rope to
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