A classifying invariant of knots, the knot quandle

Abstract The two operations of conjugation in a group, x▷y=y -1 xy and x▷ -1 y=yxy -1 satisfy certain identities. A set with two operations satisfying these identities is called a quandle. The Wirtinger presentation of the knot group involves only relations of the form y -1 xy = z and so may be construed as presenting a quandle rather than a group. This quandle, called the knot quandle, is not only an invariant of the knot, but in fact a classifying invariant of the knot.