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 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.
- applied topology
- real algebraic knot theory
- Morse-Novikov number
- knotted fields
- constructive approach to knot theory