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 the knot, constructed from a set of curves on a Seifert surface of genus "g" which represent a basis for the first homology of the surface. This means that "V" is a 2"g" × 2"g" matrix with the property that "V" − "V" is a symplectic matrix. The "Arf invariant" of the knot is the residue of Specifically, if formula_3, is a symplectic basis for the intersection form on the Seifert surface, then where formula_5 denotes the positive pushoff of "a". This approach to the Arf invariant is due to Louis Kauffman. We define two knots to be pass equivalent