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.