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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, Knot Move, Pass Move, Trefoil Knot, Unknot

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References

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

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Pass Equivalent

Cite this as:

Weisstein, Eric W. "Pass Equivalent." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PassEquivalent.html

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