On Alexander modules and Blanchfield forms of null-homologous knots in rational homology spheres

摘要

In this paper, we give a classification of Alexander modules of null-homologous knots in rational homology spheres. We characterize these modules A equipped with their Blanchfield forms φ, and the modules A such that there is a unique isomorphism class of (A, φ), and we prove that for the other modules A, there are infinitely many such classes. We realize all these (A, φ) by explicit knots in Q-spheres.