Signatures of Covering Links

A (tame) knot kn in S 3 is said to have period n if there exists a homeomorphism ϕ: S 3 → S 3, necessarily orientationpreserving, such that (i) the fixed point set of ϕ is a circle disjoint from kn (ii) ϕ(kn ) = kn ; (iii) ϕ has order n. Several necessary conditions for a knot to have period n have already been established in the literature; see [3] [11] [14] [18]. Here we establish the following further condition, involving the signature σ(kn ) of (kn ).