Cowboy bowline Various tests of the different versions' strengths show little difference; conjecture about either knot's vulnerability to some failure remain pretty much only that – conjectures. As for the tail of a regular bowline finishing "inside the loop [ eye]", that is more a formal-image state than one of an actual knot, as the draw of the standing part will pull the tail around so that it actually points away from the eye, but there are various ways the knot can be dressed to affect this aspect. There is a rule of thumb which states that the loose end should be
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