The arf invariant is a link invariant that 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

(Jones 1985). Here, the
factor takes care of the ambiguity introduced by the fact that the Alexander
polynomial is defined only up to multiples of . (Alternately, this indeterminacy is also taken care
of by the Conway definition of the polynomial.)