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 Signature of a knot The signature of a knot is a topological invariant in knot theory. It may be computed from the Seifert surface. Given a knot "K" in the 3-sphere, it has a Seifert surface "S" whose boundary is "K". The Seifert form of "S" is the pairing formula_1 given by taking the linking number formula_2 where formula_3 and formula_4 indicate the translates of "a" and "b" respectively in the positive and negative directions of the normal bundle to "S". Given a basis formula_5 for formula_6 (where "g" is the genus of the surface) the Seifert form can be