Cowboy bowline Various tests of the different versions' strengths show little difference; conjecture about either knot's vulnerability to some failure remain pretty much only that – conjectures. As for the tail of a regular bowline finishing "inside the loop [ eye]", that is more a formal-image state than one of an actual knot, as the draw of the standing part will pull the tail around so that it actually points away from the eye, but there are various ways the knot can be dressed to affect this aspect. There is a rule of thumb which states that the loose end should be
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