Isomorphic periodic links as coverings

Abstract

In this paper, we introduce a method to construct all Z(n)-coverings of a given link L and characterize them up to covering isomorphism. By using this characterization, we show that the number of the isomorphism classes of Z(n)-coverings of a link L is equal to the number of crossings of L plus one. As a result, we give a new combinatorial computing of the signature of a periodic link. A counting method for the number of the components of a periodic link is also discussed.