# A classifying invariant of knots, the knot quandle

@article{Joyce1982ACI, title={A classifying invariant of knots, the knot quandle}, author={David Joyce}, journal={Journal of Pure and Applied Algebra}, year={1982}, volume={23}, pages={37-65} }

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.

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