Moscow Mathematical Journal

Volume 24, Issue 3, July–September 2024 pp. 427–440.

$\mathbb C$-Boundary Links up to Six Crossings

Authors: S. Yu. Orevkov (1)
Author institution:(1) Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia;
IMT, L'Université Paul Sabatier, 118 route de Narbonne, Toulouse, France

Summary:

An oriented link is called $\mathbb{C}$-boundary if it is realizable as $(\partial B,A\cap\partial B)$, where $A$ is an algebraic curve in $\mathbb{C}^2$ and $B$ is an embedded $4$-ball. This notion was introduced by Michel Boileau and Lee Rudolph in 1995. In a recent joint paper with N. G. Kruzhilin we gave a complete classification of $\mathbb{C}$-boundaries with at most 5 crossings. In the present paper a more regular method of construction of $\mathbb{C}$-boundaries is proposed and the classification is extended up to 6 crossings.

2020 Math. Subj. Class. 57K10.

Keywords: $\mathbb{C}$-boundary link, slice genus, 6-crossing links.

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