History of knotting History of knotting Knots and knotting have been used and studied throughout history. For example, Chinese knotting is a decorative handicraft art that began as a form of Chinese folk art in the Tang and Song Dynasty (960-1279 AD) in China, later popularized in the Ming. Knot theory is the recent mathematical study of unknots. Knots of ancient origin include the bottle sling, bowline, cat's paw, clove hitch, cow hitch, double fisherman's knot, eskimo bowline, figure-eight knot, fisherman's knot, half hitch, kalmyk loop, one-sided overhand bend, overhand knot, overhand loop, reef knot, running bowline, single hitch, thief knot, Turk's head
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