Knots in Four Dimensions and the Fundamental Group

Authors

Jeff Boersema, Seattle UniversityFollow
Erica Whitaker, Ohio State UniversityFollow

Abstract

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.

Author Bio

Jeff Boersema and Erica (Taylor) Whitaker wrote this paper during the summer of 1992 during an NSF-sponsored Research Experiences for Undergraduates program at Calvin and Hope Colleges under the supervision of Dr. Gerard Venema. At the time, Jeff was about to be a senior at Calvin College. He is now on the faculty at Seattle University.

Jeff Boersema and Erica (Taylor) Whitaker wrote this paper during the summer of 1992 during an NSF-sponsored Research Experiences for Undergraduates program at Calvin and Hope Colleges under the supervision of Dr. Gerard Venema. At the time, Erica was about to be a senior at Birmingham-Southern College where she graduated in 1993. Currently she is in graduate school at Ohio State University.

Faculty Sponsor

Gerard A. Venema

Recommended Citation

Boersema, Jeff and Whitaker, Erica (2003) "Knots in Four Dimensions and the Fundamental Group," Rose-Hulman Undergraduate Mathematics Journal: Vol. 4: Iss. 2, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol4/iss2/2