Introduction to high dimensional knots

TL;DR

This paper provides an accessible introduction to high dimensional knot theory, covering fundamental concepts, existence of nontrivial knots, and basic operations like local moves and projections, aimed at beginners.

Contribution

It offers a simplified overview of high dimensional knots, including foundational questions and basic techniques, for readers new to the field.

Findings

Existence of nontrivial high dimensional knots confirmed

Explanation of local moves on high dimensional knots

Discussion of projections of high dimensional knots

Abstract

This is an introductory article on high dimensional knots for the beginners. High dimensional knot theory is an exciting field. It is a field of knot theory, which is one of topology and is connected with many ones. In this article we use few literal expressions, equations, functions, etc. We barely suppose that the readers have studied manifolds, homology theory, or topics beyond them. Is there a nontrivial high dimensional knot? We first answer this question. After that, we explain local moves on high dimensional knots and the projections of high dimensional knots.