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Constructing links of isolated singularities of polynomials $\mathbb{R}^4\to\mathbb{R}^2$

B. Bode

Published 2017 in Unknown venue

ABSTRACT

We show that if a braid $B$ can be parametrised in a certain way, then previous work can be extended to a construction of a polynomial $f:\mathbb{R}^4\to\mathbb{R}^2$ 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 $S^1$.

PUBLICATION RECORD

  • Publication year

    2017

  • Venue

    Unknown venue

  • Publication date

    2017-05-25

  • Fields of study

    Mathematics

  • Identifiers
    arXiv 1705.09255
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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