The Links–Gould polynomial as a generalization of the Alexander–Conway polynomial

Atsushi Ishii

Vol. 225 (2006), No. 2, 273–285

DOI: 10.2140/pjm.2006.225.273

Abstract

We show that the Alexander–Conway polynomial is recoverable from the Links–Gould (LG) polynomial via a certain reduction, and hence that the LG polynomial is a generalization of the Alexander–Conway polynomial. Furthermore, the LG polynomial inherits some properties of the Alexander–Conway polynomial. For example, the LG polynomial is a Laurent polynomial in a particular pair of symmetric variables, and this is related to a symmetry of the Alexander–Conway polynomial.

Keywords

Links–Gould link invariant, Alexander–Conway polynomial, quantum superalgebra

Mathematical Subject Classification 2000

Primary: 57M27

Milestones

Received: 4 August 2004

Revised: 13 March 2005

Accepted: 25 March 2005

Published: 1 June 2006