Strong periodicity of links and the coefficients of the Conway polynomial

Przytycki and Sokolov proved that a three-manifold admits a semi-free action of the finite cyclic group of order with a circle as the set of fixed points if and only if is obtained from the three-sphere by surgery along a strongly -periodic link . Moreover, if the quotient three-manifold is an integral homology sphere, then we may assume that is orbitally separated. This paper studies the behavior of the coefficients of the Conway polynomial of such a link. Namely, we prove that if is a strongly -periodic orbitally separated link and is an odd prime, then the coefficient is congruent to zero modulo for all such that .