A Link invariant which always has the value 0 or 1. 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. If , , and
are projections which are identical outside the region of the crossing diagram, and and are Knots while is a 2-component Link with a nonintersecting crossing diagram where the two left and right strands
belong to the different Links, then

(1) |

(2) |

(3) |

**References**

Adams, C. C. *The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.* New York:
W. H. Freeman, pp. 223-231, 1994.

Jones, V. ``A Polynomial Invariant for Knots via von Neumann Algebras.'' *Bull. Amer. Math. Soc.* **12**, 103-111, 1985.

Weisstein, E. W. ``Knots.'' Mathematica notebook Knots.m.

© 1996-9

1999-05-25