Uni knot Uni knot The uni knot is a multi purpose fishing knot that can be used for attaching the fishing line to the arbor of a reel, for joining lines, and for attaching lures, snaps, and swivels. The knot, shown with three passes, was published in 1944 under the name gallows knot (#1121) in The Ashley Book of Knots. Ashley notes that it is actually an alternate arrangement of the multiple overhand noose. His diagram shows how the knot can be manipulated into the more familiar form. This knot is also called the Duncan loop, after Norman Duncan who developed it
Arf invariant of a knot graph associated to a knot diagram. This approach to the Arf invariant is by Raymond Robertello. Let be the Alexander polynomial of the knot. Then the Arf invariant is the residue of modulo 2, where "r" = 0 for "n" odd, and "r" = 1 for "n" even. Kunio Murasugi proved that the Arf invariant is zero if and only if Δ(−1) formula_8 ±1 modulo 8. From the Fox-Milnor criterion, which tells us that the Alexander polynomial of a slice knot formula_9 factors as formula_10 for some polynomial formula_11 with integer coefficients, we know that the determinant formula_12 of a