A Generalization of Pretzel Links via Spatial Graphs

TL;DR

This paper introduces graph-pretzel links, a new class of spatial graph-based links, and demonstrates their ability to produce infinite ribbon knots distinguishable by Jones polynomials despite trivial Alexander polynomials.

Contribution

It generalizes pretzel links through spatial graphs and constructs an infinite family of ribbon knots with unique Jones polynomials.

Findings

Constructed an infinite family of ribbon knots

All knots have trivial Alexander polynomial

Knots distinguished by Jones polynomial

Abstract

In this paper, we introduce \textit{graph-pretzel links}, a generalization of classical pretzel links based on spatial graph projections. As our main result, we investigate a subfamily associated with the complete graph on four vertices to construct an infinite family of distinct ribbon knots. Furthermore, although they all share a trivial Alexander polynomial, they can be distinguished from one another by their Jones polynomials.