Applications of the Jones Polynomial

Abstract

The purpose of this expository thesis is to state and prove recent results in the theory of knots and links. In particular, we define and study the Jones polynomial. Some of its more important achievements include the proofs of the first two famous Tait conjectures. We also show some short- comings of the Jones polynomial. We exhibit infinitely many links which share the same Jones polynomial. There exist infinite families of links that have the same Jones polynomial as the unlink of n components for all n ≥ 2. We will discuss in detail such a family for n = 2.