The stable 4-genus of alternating knots

TL;DR

This paper investigates the relationship between the genus and the stable topological 4-genus of alternating knots, establishing a clear lower bound on their difference.

Contribution

It proves that the difference between the genus and the stable topological 4-genus of alternating knots is either zero or at least one-third, clarifying their quantitative relationship.

Findings

The difference is either zero or ≥ 1/3 for alternating knots.

Provides a new lower bound on the difference between genus and stable 4-genus.

Enhances understanding of the topological properties of alternating knots.

Abstract

We show that the difference between the genus and the stable topological 4-genus of alternating knots is either zero or at least 1/3.