French bowline French bowline Some consider that a French bowline is the same as a Portuguese bowline, i.e. a bowline with two loops that can be used as a bosun's chair. A different knot is however also known as a French bowline. This form of bowline is similar to a standard bowline but there are several loops so that there is less likelihood of damage to a delicate object secured by the bowline. As with a standard bowline, the knot cannot tighten. Pressure is distributed over a wider area than in the case of a standard bowline. The main advantage of this
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