Triple bowline larger than the two equal-sized loops. The size of the third loop depends on the length of the bight pulled through the loop. A bowline on the bight is a similar knot to the triple bowline. Instead of wrapping the bight around the standing end and then passing it back through the nipping loop, the two loops are passed through the bight so that it tightens on the standing end. It has only two active or available loops. This is used in rescue situations, especially in a case where there might be an injured person or people, as it forms
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