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Publication - Professor Mark Dennis

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

    Citation

    Bode, B & Dennis, M, 2019, ‘Constructing a polynomial whose nodal set is any prescribed knot or link’. Journal of Knot Theory and its Ramifications, vol 28.

    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 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.

    Full details in the University publications repository