Triple bowline Triple bowline The triple bowline knot is a variation of the bowline knot. The knot can be applied to emergency situations, such as mountain rescue. The name comes from the three loops that would be formed by tying this knot. The knot is tied in the same way the original bowline is, except with a doubled rope (using a bight). An overhand loop is formed in the rope, the working end is passed back through that loop, behind the standing part of the rope, back through the loop and pulled tight. The working end (bight) forms a third loop, often
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