Karash double loop Karash double loop Karash double loop is a common name for a knot forming two loops. This knot has been a known variant of the Bowline on a bight per the International Guild of Knot Tyers, referred to as "bowline twist" or "twisted collar bowline on a bight". The knot is also referred to as "nœud de fusion" in French references and sometimes called "Fusion knot" in English. The name "Karash double loop" was introduced by Mike Karash, who re-invented the knot to create makeshift harnesses for rescue operations and popularized it among rescue workers. The knot is used for
Arf invariant of a knot if they are related by a finite sequence of pass-moves, which are illustrated below: (no figure right now) Every knot is pass-equivalent to either the unknot or the trefoil; these two knots are not pass-equivalent and additionally, the right- and left-handed trefoils are pass-equivalent. Now we can define the Arf invariant of a knot to be 0 if it is pass-equivalent to the unknot, or 1 if it is pass-equivalent to the trefoil. This definition is equivalent to the one above. Vaughan Jones showed that the Arf invariant can be obtained by taking the partition function of a signed planar