Bowline on a bight as a seat while being hoisted as there are two secure loops as opposed to the traditional one loop bowline. In theory, this knot would make hoisting many people with one line possible. This knot is very popular in caving as it allows the load to be spread between two anchor points, reducing the stress placed on them and providing a backup should one fail. Commonly known as the Y-hang it allows for a free-hang descent and can be easily adjusted to avoid waterfalls or rub points. As mentioned earlier, this knot can replace the figure-eight knot when tying into
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