Parametrizing some interesting knotted surfaces

TL;DR

This paper presents methods for constructing polynomial parametrizations of various knotted surfaces, including spheres, tori, and planes, with specific examples illustrating these techniques.

Contribution

It introduces new methods for polynomial parametrization of knotted surfaces and provides explicit examples demonstrating their application.

Findings

Polynomial parametrizations for knotted spheres, tori, and planes are constructed.

Explicit examples of knotted surfaces with polynomial parametrizations are provided.

The methods facilitate visualization and further study of knotted surfaces.

Abstract

We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.