On Jones polynomials of alternating pretzel knots

TL;DR

This paper proves that infinitely many pairs of alternating pretzel knots share the same Jones polynomial, highlighting limitations in using Jones polynomials to distinguish such knots.

Contribution

It demonstrates the existence of infinitely many distinct alternating pretzel knots with identical Jones polynomials, revealing a new limitation of this knot invariant.

Findings

Infinitely many pairs of alternating pretzel knots have identical Jones polynomials.

Jones polynomial cannot distinguish all alternating pretzel knots.

The result challenges the uniqueness of Jones polynomials for certain knot classes.

Abstract

We show that there are infinitely many pairs of alternating pretzel knots whose Jones polynomials are identical.