A classifying invariant of knots, the knot quandle

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Abstract

The two operations of conjugation in a group, x▷y=y-1xy and x▷-1y=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-1xy=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.

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