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

Benjamin Bode, Mark Dennis

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
128 Downloads (Pure)

Abstract

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.

Original languageEnglish
Article number1850082
JournalJournal of Knot Theory and its Ramifications
Volume28
Issue number1
DOIs
Publication statusPublished - 10 Jan 2019

Keywords

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

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