Jones polynomial

In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable ${\displaystyle t^{1/2}}$ with integer coefficients.

Suppose we have an oriented link ${\displaystyle L}$, given as a knot diagram. We will define the Jones polynomial, ${\displaystyle V(L)}$, using Kauffman's bracket polynomial, which we denote by ${\displaystyle \langle ~\rangle }$. Note that here the bracket polynomial is a Laurent polynomial in the variable ${\displaystyle A}$ with integer coefficients.

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