Yosemite bowline knot. A stopper knot, while serving to keep the loose end tidy, will not only help to prevent failure of the primary knot, but also act as a secondary safety knot itself. It is sometimes said that if enough of a tail is left to tie a stopper knot, the stopper becomes unnecessary. The tail should be a minimum of 40–60 cm depending on the thickness of the rope. Yosemite bowline A Yosemite bowline is loop knot often perceived as having better security than a bowline. It has been pointed out that if the knot is not dressed correctly it
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