Eskimo bowline sheet bend. (The image above with red rope would result in an ends-opposite (and inferior) sheet bend; the version shown on the right side would give a same-side sheet bend (ABoK #1431). The common bowline when ring-loaded becomes effectively an inferior version of the Lapp bend, and so can slip and untie; the wrongly demeaned "left-handed"/"cowboy" bowline becomes the proper Lapp bend, and should hold.) A Cossack knot is another name for the same knot. A slipped version of the Cossack knot is called Kalmyk loop. Eskimo bowline The Eskimo bowline is an 'anti-bowline' which is in a class of
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