Detection of Chirality and Mutations of Knots and Links

TL;DR

This paper explores using Chern-Simons gauge theory to detect chirality and mutations in knots and links, demonstrating that generalized knot invariants outperform traditional polynomials, though knot classification remains challenging.

Contribution

It introduces a method leveraging Chern-Simons gauge theory to improve detection of knot properties beyond existing polynomial invariants.

Findings

Generalized knot invariants are more powerful than Jones, HOMFLYPT, and Kauffman polynomials.

Detection of chirality and mutations is feasible with these invariants.

Knot classification remains an open problem.

Abstract

In this brief presentation, we would like to present our attempts of detecting chirality and mutations from Chern-Simons gauge theory. The results show that the generalised knot invariants, obtained from Chern-Simons gauge theory, are more powerful than Jones, HOMFLYPT and Kauffman polynomials. However the classification problem of knots and links is still an open challenging problem.