2022/11/22 by Benjamin Bode, Bode, Benjamin
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2211.12329
Semiholomorphic polynomials are functions f:ℂ2→ℂ that can be written as polynomials in complex variables u, v and the complex conjugate v. We prove the semiholomorphic analogoue of Akbulut's and King's "All knots are algebraic", that is, every link type in the 3-sphere arises as the link of a weakly isolated singularity of a semiholomorphic polynomial. Our proof is constructive, which allows us to obtain an upper bound on the polynomial degree of the constructed functions.