Knot modules and ribbon 2-knots

TL;DR

This paper demonstrates that all torsion-free knot modules can be realized by ribbon 2-knots with low-dimensional groups and explores their properties, especially for fibred ribbon 2-knots.

Contribution

It establishes realization results for torsion-free knot modules via ribbon 2-knots and provides partial characterizations of fibred ribbon 2-knot modules.

Findings

Every torsion-free knot module is realized by a ribbon 2-knot.

Ribbon 2-knots have groups of geometric dimension at most 2.

Partial results on the characterization of fibred ribbon 2-knot modules.

Abstract

We show that every $\mathbb{Z}$-torsion free knot module is realized by a ribbon 2-knot with group of geometric dimension at most 2, and give some partial results on the characterization of the knot modules of fibred ribbon 2-knots.