The Theory of Braids

Abstract

At the beginning of the 1930s, as a means of studying knots, E. Artin introduced a concept of a (mathematical) braid(s). This remarkable insight itself was not sufficient to sustain research in this area, and so it slowly began to wither. However, in the 1950s this concept of braids was found to have applications in other fields, and this gave fresh impetus to the study of braids, rekindling research in this area. The iridescent hue of this concept flowering into full bloom and activity occurred in 1984, when V. Jones put into action with inordinate success the original aim of Artin, i.e., the application of braids to knot theory. In this chapter our intention is to introduce certain necessary aspects of the theory of braids that will prove useful when we explain recent developments in knot theory in the subsequent chapters.