Constructing a polynomial whose nodal set is any prescribed knot or link

We describe an algorithm that for every given braid B explicitly constructs a function f:C2 → C such that f is a polynomial in u, v and v̄ 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.