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

Benjamin Bode, Mark Dennis

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 Citations (Scopus)
107 Downloads (Pure)


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.
Original languageEnglish
Article number1850082
Number of pages31
JournalJournal of Knot Theory and its Ramifications
Issue number1
Early online date10 Jan 2019
Publication statusPublished - Jan 2019

Structured keywords



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


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