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 graph associated to a knot diagram. This approach to the Arf invariant is by Raymond Robertello. Let be the Alexander polynomial of the knot. Then the Arf invariant is the residue of modulo 2, where "r" = 0 for "n" odd, and "r" = 1 for "n" even. Kunio Murasugi proved that the Arf invariant is zero if and only if Δ(−1) formula_8 ±1 modulo 8. From the Fox-Milnor criterion, which tells us that the Alexander polynomial of a slice knot formula_9 factors as formula_10 for some polynomial formula_11 with integer coefficients, we know that the determinant formula_12 of a