Polynomially knotted 2-spheres

TL;DR

This paper reviews polynomial parameterizations of classical knots, extends these results to long 2-knots, and constructs polynomial models for specific knotted spheres like spun and twist spun knots.

Contribution

It introduces polynomial parameterizations for long 2-knots and certain knotted spheres, expanding the scope of polynomial knot theory.

Findings

Polynomial parameterizations exist for long 2-knots.

Constructed polynomial models for spun and twist spun knotted spheres.

Extended classical knot results to higher-dimensional knotted spheres.

Abstract

We review the polynomial parameterization of classical knots and prove the analogous results for long $2$ knots. We also construct polynomial parameterizations for certain classes of knotted spheres (such as spun and twist spun of the classical knots).