Alexander and Thurston Norms of Graph Links

We show that the Alexander and Thurston norms are the same for all irreducible Eisenbud-Neumann graph links in homology 3-spheres. These are the links obtained by splicing Seifert links in homology 3-spheres together along tori. By combining this result with previous results, we prove that the two norms coincide for all links in S3 if either of the following two conditions are met; the link is a graph link, so that the JSJ decomposition of its complement in S3 is made up of pieces which are all Seifert-fibered, or the link is alternating and not a (2, n)-torus link, so that the JSJ decomposition of its complement in S3 is made up of pieces which are all hyperbolic. We use the E-N obstructions to fibrations for graph links together with the Thurston cone theorem on link fibrations to deduce that every facet of the reduced Thurston norm unit ball of a graph link is a fibered facet.