A transcendental function invariant of virtual knots

TL;DR

This paper introduces a new transcendental function invariant for virtual knots that generalizes multiple existing polynomial invariants, providing a potentially more powerful tool for knot classification.

Contribution

The paper presents a novel invariant for virtual knots, extending the scope of polynomial invariants through a transcendental function approach.

Findings

The invariant generalizes the writhe polynomial, affine index polynomial, and zero polynomial.

It offers a new perspective on virtual knot invariants.

Potential for improved knot distinction capabilities.

Abstract

In this work we describe a new invariant of virtual knots. We show that this transcendental function invariant generalizes several polynomial invariants of virtual knots, such as the writhe polynomial, the affine index polynomial and the zero polynomial.