2 research outputs found
Knots in Four Dimensions and the Fundamental Group
This paper is an introduction to knotted spheres in four dimensions (analogous to knotted circles in three dimensions). We define what a knotted sphere is and describe a to visually represent them, via movies. The fundamental group of the complement of a knot is a powerful invariant and we describe this invariant in detail giving a convenient algorithm for computing it. Lots of examples are given, including the simplest non-trivial locally flat knot