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 represented as a "2g"-by-"2g" Seifert matrix "V", formula_7. The signature of the matrix formula_8, thought of as a symmetric bilinear form, is the signature of the knot "K". Slice knots are known to have zero signature. Knot signatures can also be defined in terms of the Alexander module of the knot complement. Let formula_9 be the universal abelian cover of the knot complement. Consider the Alexander module to be the first homology group of the universal abelian cover of the knot complement: formula_10. Given a formula_11-module formula_12, let formula_13 denote the formula_11-module whose underlying formula_15-module is formula_12 but where formula_17