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.
Gerard A. Venema - Department of Mathematics and StatisticsCalvin College, Grand Rapids, MI email@example.com
Boersema, Jeff and Whitaker, Erica
"Knots in Four Dimensions and the Fundamental Group,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 4
, Article 2.
Available at: http://scholar.rose-hulman.edu/rhumj/vol4/iss2/2