Climbing harness the purpose, primarily a variation of the double bowline, but the figure-eight is usually preferred. Although it is harder to untie after a fall, it is inherently more secure, easier to tie, and easier to verify that it has been tied correctly. There are many variations of the bowline knot, and some will untie themselves when repeatedly stressed and unstressed, as is common in climbing. In addition to the weight bearing parts of the harness, there are parts of the harness that are not designed to be part of the safety system. These include the gear loops, used for carrying
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