Alexander and Thurston norms of graph links

Abstract

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 S^3 if either of the following two conditions are met; the link is a graph link, so that the JSJ decomposition of its complement in S^3 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 S^3 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.