The Jones Polynomial and its Limitations

TL;DR

This paper explores the Kauffman bracket model of the Jones polynomial, discusses tangle-based computation methods, and demonstrates the polynomial's limitations in detecting certain non-trivial links.

Contribution

It provides an exposition of the Kauffman bracket approach and introduces tangle methods to identify links undetectable by the Jones polynomial.

Findings

Identification of non-trivial links not detected by the Jones polynomial

Explanation of tangle methods for computing the Jones polynomial

Analysis of the limitations of the Jones polynomial in link detection

Abstract

This paper will be an exposition of the Kauffman bracket polynomial model of the Jones polynomial, tangle methods for computing the Jones polynomial, and the use of these methods to produce non-trivial links that cannot be detected by the Jones polynomial.