The Links-Gould invariant as a classical generalization of the Alexander polynomial?

TL;DR

This paper explores the Links-Gould invariant, proposing it as a classical generalization of the Alexander polynomial, and investigates its potential to estimate link genus and determine fiberedness, supported by preliminary evidence.

Contribution

It conjectures that the Links-Gould invariant shares classical features with the Alexander polynomial, such as bounding genus and indicating fiberedness, and provides initial evidence for these properties.

Findings

Links-Gould invariant may bound the genus of links

It could serve as a criterion for fibered knots

Preliminary evidence supports these conjectures

Abstract

In this paper we conjecture that the Links-Gould invariant of links, that we know is a generalization of the Alexander-Conway polynomial, shares some of its classical features. In particular it seems to give a lower bound for the genus of links and to provide a criterion for fiberedness of knots. We give some evidence for these two assumptions.