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
Signature of a knot formula_11. This form takes value in the rational polynomials whose denominators are the Alexander polynomial of the knot, which as a formula_11-module is isomorphic to formula_34. Let formula_35 be any linear function which is invariant under the involution formula_36, then composing it with the sesquilinear duality pairing gives a symmetric bilinear form on formula_37 whose signature is an invariant of the knot. All such signatures are concordance invariants, so all signatures of slice knots are zero. The sesquilinear duality pairing respects the prime-power decomposition of formula_37—i.e.: the prime power decomposition gives an orthogonal decomposition of formula_39. Cherry Kearton has shown