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 the knot, constructed from a set of curves on a Seifert surface of genus "g" which represent a basis for the first homology of the surface. This means that "V" is a 2"g" × 2"g" matrix with the property that "V" − "V" is a symplectic matrix. The "Arf invariant" of the knot is the residue of Specifically, if formula_3, is a symplectic basis for the intersection form on the Seifert surface, then where formula_5 denotes the positive pushoff of "a". This approach to the Arf invariant is due to Louis Kauffman. We define two knots to be pass equivalent