Strong periodicity of links and the coefficients of the Conway polynomial

الأصل · EN

Przytycki and Sokolov proved that a three-manifold admits a semi-free action of the finite cyclic group of order p with a circle as the set of fixed points if and only if M is obtained from the three-sphere by surgery along a strongly p-periodic link L. Moreover, if the quotient three-manifold is an integral homology sphere, then we may assume that L is orbitally separated. This paper studies the behavior of the coefficients of the Conway polynomial of such a link. Namely, we prove that if L is a strongly p-periodic orbitally separated link and p is an odd prime, then the coefficient a₂ᵢ(L) is congruent to zero modulo p for all i such that 2i<p-1.