Seifert matrices of periodic knots

Abstract

We characterize the Seifert matrices of periodic knots in $S^3$ and realize periodic knots with prescribed Seifert matrices satisfying our characterization that reflects the periodicity of the knot K and contains information only on the Seifert matrix of the factor knot~$\bar K$ of K and the way how $\bar K$ links the axis of the periodic action. As an application, we give an alternative proof that the Alexander polynomials of periodic knots satisfy the Murasugi condition.