Link signature, Goeritz matrices and polynomial invariants
type: Item
instance of: scholarly article
title: Link signature, Goeritz matrices and polynomial invariants
zbMATH Open document ID: 0711.57004
published in: L'Enseignement Mathématique. 2e Série
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4169671
zbMATH Keywords: Kauffman polynomial
zbMATH Keywords: writhe of a diagram
zbMATH Keywords: link signature function
zbMATH Keywords: skein invariant
zbMATH Keywords: Alexander polynomial
zbMATH Keywords: concordance
zbMATH Keywords: graph of a link
zbMATH Keywords: Goeritz matrix
author: Andrew S. Lipson
reviewed by: Yasuhiro Nakagawa
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4169671