The Fundamental Group of Torus Knots

Abstract

This work is concerned with the calculation of the fundamental group of torus knots. Torus knots are special types of knots which wind around a torus a number of times in the longitudinal and meridional directions. We compute and describe the fundamental group of torus knots by using some concepts in algebraic topology and group theory. We also calculate the fundamental group of an arbitrary knot by using an algorithm called the Wirtinger presentation.