Constructing links of isolated singularities of polynomials\n \ℝ⁴\→\ℝ²

2017/05/25 by Benjamin Bode, Bode, Benjamin
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1705.09255

openalex publication_date 2017/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if a braid B can be parametrised in a certain way, then\nprevious work can be extended to a construction of a polynomial\nf:\ℝ⁴\→\ℝ² with the closure of B as the link of an\nisolated singularity of f, showing that the closure of B is real algebraic.\nIn particular, we prove that closures of squares of strictly homogeneous braids\nand certain lemniscate links are real algebraic. We also show that the\nconstructed polynomials satisfy the strong Milnor condition, providing an\nexplicit fibration of the complement of the closure of B over S¹.\n

Citations

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

Related

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