Triple bowline Triple bowline The triple bowline knot is a variation of the bowline knot. The knot can be applied to emergency situations, such as mountain rescue. The name comes from the three loops that would be formed by tying this knot. The knot is tied in the same way the original bowline is, except with a doubled rope (using a bight). An overhand loop is formed in the rope, the working end is passed back through that loop, behind the standing part of the rope, back through the loop and pulled tight. The working end (bight) forms a third loop, often
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