Knot cavers, arborists, rescue professionals, stagehands, fishermen, linemen and surgeons. The International Guild of Knot Tyers is an organization dedicated to the Promotion of Knot tying. Truckers in need of securing a load may use a trucker's hitch, gaining mechanical advantage. Knots can save spelunkers from being buried under rock. Many knots can also be used as makeshift tools, for example, the bowline can be used as a rescue loop, and the munter hitch can be used for belaying. The diamond hitch was widely used to tie packages on to donkeys and mules. In hazardous environments such as mountains, knots are
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