Power series link invariants and the Thurston norm
In [\textit{E. Kalfagianni} and \textit{X.-S. Lin}, The HOMFLY polynomial for links in rational homology spheres, Topology 38, No. 1, 95-115 (1999)] power series invariants for links in certain \(\mathbb{Z}\)-homology spheres were constructed which satisfy a skein relation. For \(S^3\) these power series converge to Laurent polynomials (the 2-variable polynomials). A class of links (infinite links) is defined which represents an obstruction to the convergence in an irreducible homology sphere. As a tool a generalization of the Scharlemann-Thompson relation between the Euler characteristics of skein-partners \(L_+,L_-,L_0\) is proved.
scientific article; zbMATH DE number 1395049