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}
}
  • D. Joyce
  • Published 1982
  • Mathematics
  • Journal of Pure and Applied Algebra
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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