Tom fool's knot Tom fool's knot The Tom fool's knot is sometimes considered a handcuff knot but is somewhat inferior for this purpose to the knot which usually bears that name. It is a good knot with which to commence a slightly fancy sheepshank. It is also used as a trick knot due to the speed with which it can be made. Tom fool's knot is believed to be the knot "epankylotos brokhos" described by the 1st Century Greek physician Heraklas. It is formed by making two loops, not exactly overlaying each other. The inner half of each hitch or loop is pulled
Signature of a knot formula_11. This form takes value in the rational polynomials whose denominators are the Alexander polynomial of the knot, which as a formula_11-module is isomorphic to formula_34. Let formula_35 be any linear function which is invariant under the involution formula_36, then composing it with the sesquilinear duality pairing gives a symmetric bilinear form on formula_37 whose signature is an invariant of the knot. All such signatures are concordance invariants, so all signatures of slice knots are zero. The sesquilinear duality pairing respects the prime-power decomposition of formula_37—i.e.: the prime power decomposition gives an orthogonal decomposition of formula_39. Cherry Kearton has shown