A lower bound on the stable 4-genus of knots

TL;DR

This paper establishes a new lower bound on the stable 4-genus of knots using Casson-Gordon signatures, computes it for twist knots, and relates torsion in the concordance group to the stable 4-genus.

Contribution

It introduces a novel lower bound on the stable 4-genus based on Casson-Gordon signatures and applies it to an infinite family of knots, revealing new insights into knot torsion.

Findings

Lower bound on stable 4-genus for twist knots

Twist knot torsion characterized by vanishing stable 4-genus

Explicit computation of bounds for an infinite family

Abstract

We present a lower bound on the stable $4$-genus of a knot based on Casson-Gordon $\tau$-signatures. We compute the lower bound for an infinite family of knots, the twist knots, and show that a twist knot is torsion in the knot concordance group if and only if it has vanishing stable $4$-genus.