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A (tame) knot k n 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 k n (ii) ϕ ( k n ) = k n ; (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 ( k n ) of ( k n ).
Gordon et al. (Wed,) studied this question.
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