Link signature, Goeritz matrices and polynomial invariants
In the first part of this paper, the author shows that the link signature function \(\sigma_ L: S^ 1\to Z\) is a skein invariant for links with nonzero Alexander polynomial. He mentions that it is natural to ask what relations there may be between skein theory and concordance theory, since \(\sigma_ L(\omega)\) is known to be a concordance invariant. In the second part, he studies the relationships between the graph of a link, its Goeritz matrix and Kauffman's polynomial invariant \(F_ L(a,z)\). Then he shows that a renormalized form of Kauffman's polynomial invariant \(F_ L(a,z)\), well-defined on non-oriented links, is calculable from the Goeritz matrix. He raises the question of what relation there is between \(F_ L(a,z)\) and the quadratic forms represented by Goeritz matrices.
scientific article; zbMATH DE number 4169671