A Note on a Map from Knots to $2$-Knots

TL;DR

This paper introduces a mathematical map linking classical knots to 2-knots, extending to higher dimensions, and connects it to the braid theory of specific groups, enriching the understanding of knot and braid relationships.

Contribution

It constructs a novel map from knots to 2-knots that generalizes to higher dimensions, bridging knot theory and braid group theory.

Findings

Established a natural correspondence between knots and 2-knots.

Extended the map to higher-dimensional knots.

Linked the map to the braid theory of groups G_{n}^{k}.

Abstract

We construct a map from knots to (abstract) 2-knots which can be extended to higher dimensions; this map is the natural "knot" counterpart for "braid" theory of groups $G_{n}^{k}$.