We describe an algorithm that for every given braid $B$ explicitly constructs a function $f:\mathbb{ C}^{ 2}\rightarrow\mathbb{ C}$ such that $f$ is a polynomial in $u$, $v$ and $\overline{ v}$ and the zero level set of $f$ on the unit three-sphere is the closure of $B$. The nature of this construction allows us to prove certain properties of the constructed polynomials. In particular, we provide bounds on the degree of $f$ in terms of braid data.
Categories: math.GT math-ph math.MP