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Pass Equivalent

Two Knots are pass equivalent if there exists a sequence of pass moves taking one to the other. Every Knot is either pass equivalent to the Unknot or Trefoil Knot. These two knots are not pass equivalent to each other, but the Enantiomers of the Trefoil Knot are pass equivalent. A Knot has Arf Invariant 0 if the Knot is pass equivalent to the Unknot and 1 if it is pass equivalent to the Trefoil Knot.

See also Arf Invariant, Knot, Pass Move, Trefoil Knot, Unknot


Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 223-228, 1994.

© 1996-9 Eric W. Weisstein