We show that if a braid B can be parametrized in a certain way, then the previous work (B. Bode and M. R. Dennis, Constructing a polynomial whose nodal set is any prescribed knot or link, arXiv:1612.06328) can be extended to a construction of a polynomial f: R4 → R2 with the closure of B as the link of an isolated singularity of f, showing that the closure of B is real algebraic. In particular, we prove that closures of squares of strictly homogeneous braids and certain lemniscate links are real algebraic. We also show that the constructed polynomials satisfy the strong Milnor condition, providing an explicit fibration of the complement of the closure of B over S1.
|Number of pages||21|
|Journal||Journal of Knot Theory and its Ramifications|
|Publication status||Published - 21 Jan 2019|
- homogeneous braids
- Isolated singularities
- Milnor fibration
- real algebraic links