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 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