Bowline draws tighter as tension is placed on the standing part of the rope. The "Birmingham bowline" has two loops; the working part is passed twice around the standing part (the "rabbit" makes two trips out of the hole and around the tree). Other two-loop bowline knots include the Spanish bowline and the bowline on the bight; these can be tied in the middle of a rope without access to the ends. A triple bowline is used to make three loops. A Cossack knot is a bowline where the running end goes around the loop-start rather than the main part and
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