# Definition of the cord algebra of knots using Morse Theory

## TL;DR

This paper redefines the cord algebra, a knot invariant, using Morse Theory, providing explicit calculations for the unknot and right-handed trefoil, and proving its invariance under knot isotopies.

## Contribution

The paper introduces a Morse Theory-based definition of the cord algebra and proves its invariance, offering a new perspective and computational approach for this knot invariant.

## Key findings

- Explicit cord algebra for the unknot
- Explicit cord algebra for the right-handed trefoil
- Proof of invariance under knot isotopies

## Abstract

We redefine the cord algebra, which was introduced by Lenhard Ng as a topological knot invariant, in terms of Morse Theory. The determination of the cord algebra of the unknot and of the righthanded trefoil are given. We proove that the cord algebra in our definition is a knot invariant.