Power series link invariants and the Thurston norm

We generalize a result of Scharlemann and Thompson (1989) to obtain a relation between the Thurston norms of links related by “skein moves”, in irreducible homology 3-spheres. Then we apply this result to the study of “skein trees” of links and we formulate an obstruction to the convergence of the HOMFLY power series link invariants constructed by Kalfagianni and Lin (1998).