New Link Invariants and Yang-Baxter Equation

TL;DR

This paper introduces new solutions to the Yang-Baxter equation, leading to novel link invariants with multiple parameters, generalizing Jones' polynomial and providing tools for knot linking analysis.

Contribution

The paper presents new Yang-Baxter solutions and constructs multi-parameter link invariants, expanding the mathematical framework for knot theory.

Findings

New solutions to the Yang-Baxter equation

Multi-parameter link invariants constructed

A simpler invariant for linking structure

Abstract

We have new solutions to the Yang-Baxter equation, from which we have constructed new link invariants containing more than two arbitrary parameters. This may be regarded as a generalization of the Jones' polynomial. We have also found another simpler invariant which discriminates only the linking structure of knots with each other, but not details of individual knot.