Bowline on a bight end(s) and tucking the bight back down beside itself. Instead, the bight is opened up to allow the whole knot to pass through it (see picture on right). When tightened, the bight now embraces the pair of standing ends (see top picture) Bowline on a bight The Bowline on a bight is a knot which makes a pair of fixed-size loops in the middle of a rope. Its advantage is that it is reasonably easy to untie after being exposed to a strain. This knot can replace the figure-eight knot when tying into a climbing harness. However, it is critical
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