Chiral Knots: An Application to Synthetic Chemistry

Abstract

The purpose of this paper is to serve as an introduction to knot theory by mathematically defining a knotand equivalent knots in 3-space, specifically in terms of topology. Via the concepts of ambient isotopy and the Kauffman X polynomial refine definition of equivalent knots. The definition of equivalence interms of the Kauffman X Polynomial has a significant application to synthetic chemistry. All of this leads us to the study of chirality, determining whether a molecule can be deformed into its mirror image. Certain molecules, especially enzymes react differently if they are chiral, means they cannot be deformed into their mirror image.

Key words: Equivalent knots, ambient isotopy, Kauffman X polynomial, chirality.