Bowline on a bight advocate the use of a figure eight twisted version of the Bowline on a bight. This knot can be used to provide a toe hold in the middle of a rope; to make an emergency bosun's chair; and to create an upper rope "block" to make a crude purchase by threading the rope round an anchor point and then back up through the loop. It is sometimes used in sport climbing to tie into two anchor bolts independently. This knot is convenient when a dependable loop is required but neither end of the line is available. It's also commonly used
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