This paper by Vaughan F. R. Jones introduces a polynomial invariant for tame oriented links using representations of the braid group. The invariant is derived from Markov's theorem, which characterizes when two braids represent the same link, and a trace formula unique to certain von Neumann algebras called type II$_1$ factors. The Alexander polynomial, which is a key invariant in knot theory, is normalized to be symmetric in $t$ and $t^{-1}$ with $\Delta(1) = 1$. This work addresses the difficulty in applying Markov's theorem and the lack of an algorithm to determine equivalence of braids, making it challenging to use braids for studying links.This paper by Vaughan F. R. Jones introduces a polynomial invariant for tame oriented links using representations of the braid group. The invariant is derived from Markov's theorem, which characterizes when two braids represent the same link, and a trace formula unique to certain von Neumann algebras called type II$_1$ factors. The Alexander polynomial, which is a key invariant in knot theory, is normalized to be symmetric in $t$ and $t^{-1}$ with $\Delta(1) = 1$. This work addresses the difficulty in applying Markov's theorem and the lack of an algorithm to determine equivalence of braids, making it challenging to use braids for studying links.