What Is Knot Theory? Why Is It In Mathematics?

Abstract

In this chapter, we briefly explain some elementary foundations of knot theory. In 1.1, we explain about knots, links and spatial graphs together with several scientific examples. In 1.2, we discuss diagrams of knots, links and spatial graphs and equivalences on knots, links and spatial graphs. Basic problems on knot theory are also explained there. In 1.3, a brief history on knot theory is stated. In 1.4, we explain how the first non-trivial knot is confirmed. In 1.5, the linking number useful to confirm a non-trivial link and the linking degree which is the absolute value of the linking number are explained. In particular, we show that the linking degree is defined directly from an unoriented link. In 1.6, some concluding remarks on this chapter are given. In 1.7, some books on knot theory are listed as general references.