nLab
surface knot

Contents

Context

Knot theory

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents

Idea

The notion of surface knots is the next higher dimensional analog of that of knots: Where a knot is a 1-dimensional submanifold of the 3d Euclidean space/3-sphere, so a surface knot is a 2-dimensional submanifold (hence a surface) of the 4d Euclidean space/4-sphere.

References

Exposition:

  • Lawrence Hook, Knots in four dimensions (pdf)

Textbook accounts:

Created on January 31, 2021 at 04:27:24. See the history of this page for a list of all contributions to it.