A lower bound for the genus of a knot using the Links-Gould invariant

2023/10/24 by Kohli, Ben-Michael, Tahar, Guillaume · 3 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2310.15617

Abstract

The Links-Gould invariant of links LG^2,1 is a two-variable generalization of the Alexander-Conway polynomial. Using representation theory of U_q\mathfrakgl(2 \vert 1), we prove that the degree of the Links-Gould polynomial provides a lower bound on the Seifert genus of any knot, therefore improving the bound known as the Seifert inequality in the case of the Alexander invariant. One practical consequence of this new genus bound is a straightforward proof of the fact that the Kinoshita-Terasaka and Conway knots have genus greater or equal to 2.

Cited by

• U_q(\mathfrakgl(m|n)) bounds on the minimal genus of virtual links
• On some log-concavity properties of the Alexander-Conway and Links-Gould invariants
• On the colored Links--Gould polynomial

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