Shoelace knot the granny (or duffer's) knot. This version will also produce asymmetrical slips; one pointing down the other up. Shoelace knot The shoelace knot, or bow knot, is commonly used for tying shoelaces and bow ties. The shoelace knot is a doubly slipped reef knot formed by joining the ends of whatever is being tied with a half hitch, folding each of the exposed ends into a loop (bight) and joining the loops with a second half hitch. The size of the loops and the length of the exposed ends are adjusted when the knot is tied. It has the stability
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