Abstract
It is shown that if a nontrivial knot K in S 3 has genus g and is invariant under a smooth action of a cyclic group C m of order m which fixes a simple closed curve disjoint from K, then K is the boundary of an invariant Seifert surface of genus g. As a corollary one has that m⩽2 g+1. The proof utilizes the theory of least area surfaces in 3-manifolds.
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