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 slice knot is a square integer. As formula_12 is an odd integer, it has to be congruent to 1 modulo 8. Combined with Murasugi's result this shows that the Arf invariant of a slice knot vanishes. Arf invariant of a knot In the mathematical field of knot theory, the Arf invariant of a knot, named after Cahit Arf, is a knot invariant obtained from a quadratic form associated to a Seifert surface. If "F" is a Seifert surface of a knot, then the homology group H("F", Z/2Z) has a quadratic form whose value is the number of full twists mod