All links are semiholomorphic

Benjamin Bode

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arXiv · 2211.12329

All links are semiholomorphic

Benjamin Bode

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Abstract

Semiholomorphic polynomials are functions $f:\mathbb{C}^2\to\mathbb{C}$ that can be written as polynomials in complex variables $u$, $v$ and the complex conjugate $\overline{v}$. 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.

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BibTeX RIS

Benjamin Bode. 2022-11-22. All links are semiholomorphic. https://arxiv.org/abs/2211.12329

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