The Arf invariant of a totally proper link (Q1058198)

The Arf invariant of a knot K in \(S^ 2\) is easily computable from its Alexander polynomial. However, since the Arf invariant of a proper n- component link L is defined as that of a knot pass equivalent to L, it is nice to find a direct way of computing the Arf invariant of L. The first formula was obtained by the reviewer for a proper 2-component link [Math. Proc. Camb. Philos. Soc. 95, 61-69 (1984; Zbl 0558.57001)]. This formula involves only the reduced Alexander polynomial of L and the Arf invariant of each component. The author of this paper generalizes the reviewer's formula for any n-component link for which all of its sublinks are also proper. The formula is described in terms of the Conway polynomial. A proof is done by induction on the number of components of L.