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
Arf invariant of a knot if they are related by a finite sequence of pass-moves, which are illustrated below: (no figure right now) Every knot is pass-equivalent to either the unknot or the trefoil; these two knots are not pass-equivalent and additionally, the right- and left-handed trefoils are pass-equivalent. Now we can define the Arf invariant of a knot to be 0 if it is pass-equivalent to the unknot, or 1 if it is pass-equivalent to the trefoil. This definition is equivalent to the one above. Vaughan Jones showed that the Arf invariant can be obtained by taking the partition function of a signed planar